## [Study Pack] Week 1 to 8 Math 225N – Statistical Reasoning for the Health Sciences # [Study Pack] Week 1 to 8 Math 225N – Statistical Reasoning for the Health Sciences

This document contains a week-by-week compilation of study materials from Math 225N. It offers a comprehensive way to go through all the course content using the weekly questions, answers, discussions and topic areas.

To get all the answers in one bundle or any specific week, get in touch via the chat window. We have worked on several versions of the questions over time.

We also week by week offer support for the MATH225N class. Get in touch for a premium package.

# MATH 225N Week 1 Assignment Comparing Sampling Methods Answers

1. A television station plans to send a crew to a polling center on an election day. Because they do not have time to interview … each individual voter, they decide to count voters leaving the polling location and ask every 20th voter for an interview. What type of sampling is this?
2. In order to study the shoe sizes of people in his town, Billy samples the population by dividing the residents by age and randomly … selecting a proportionate number of residents from each age group. Which type of sampling is … ?
3. The management of a large airline wants to estimate the average time after takeoff taken before the crew begins serving snacks and beverages on their flights. Assuming that management has easy access to all of the information that … would be required to select flights by each proposed method, which of the following would be reasonable methods of stratified sampling? Select all that apply.
4. To study the mean respiratory rate of all people in his state, Frank samples the population by dividing the residents by towns and … randomly selecting 12of the towns. He then collects data from all the residents in the selected towns. Which type of sampling is … ?
5. When is stratified sampling appropriate?
6. In reference to different sampling methods, cluster sampling includes the steps: use simple random sampling to select a set of groups; every individual in the chosen groups is included in the sample.
7. When is cluster sampling appropriate?
8. To study the mean head size of all people in her state, Jacqueline collects data from 20people in her town. Which type of sampling is … ?
9. An executive for a large national restaurant chain with multiple locations in each of 513counties wants to personally sample the … cleanliness of the chain’s restaurants throughout the country by visiting restaurants. The executive wants a good-quality sample but wants to minimize travel time and expenses. Which of the following sampling methods would be most appropriate?
10. In order to study the wrist sizes of people in her town, Kathryn samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is … ?
11. A manufacturer has three tool centers that each make about 1000tools every day. In order to implement better quality-control procedures, the manager wants to start sampling the tools made each day to be able to identify … issues as quickly as possible. Which sampling method would be most appropriate?
12. To study the mean blood pressure of all people in her state, Christine samples the population by dividing the residents by towns and randomly selecting 9of the towns. She then collects data from all the residents in the selected towns. Which type of sampling is … ?
13. When is using a simple random sample appropriate?
14. Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into groups by grade level and randomly selecting a proportionate number of students from … each group. He then collects data from the sample. Which type of sampling is … ?
15. A grocer receives cartons of 12eggs in boxes of 100 In a particular month, the grocer receives 4 shipments of eggs with 20 boxes in each shipment. The grocer wants to estimate the proportion of cartons he receives this month … that include at least one broken egg. Which of the following sampling methods … would be most appropriate?
16. When considering different sampling methods, stratified sampling includes the steps: _______

# MATH 225N Week 1 Discussion, Basic Statistics Data Used in Everyday Life

Present two different types of data, or variables, used in the health field. Examples could be blood pressure, temperature, pH, pain rating scales, pulse oximetry, % hematocrit, minute respiration, gender, age, ethnicity, etc.

Classify each of your variables as qualitative or … quantitative and explain why they fall into the category that you chose.

Also, classify each of the variables as to their level of measurement–nominal, ordinal, interval or ratio—and justify your classifications.

Which type of sampling could you use to gather your data? (stratified, cluster, systematic, and convenience sampling).

# MATH 225N Week 1 Evidence, Claims, and types Questions and Answers

1. A study is … to research the effects of drinking coffee on hours of sleep. Would an experimental or … observational study design more appropriate?
2. A researcher is … in the effects of watching videos just before bed on the quality of sleep. Which of the following claims would … appropriate for this situation? Select only one answer choice.
3. In a psychological study aimed at testing a medicine for reducing stress levels, the researcher grouped the participants into 2groups and gave the stress-reduction pill to one group and a placebo pill to another group. In the … description of the above situation, determine the experimental group.
4. In a survey conducted to find out the feedback of a sports program organized in a club, the organizers asked the respondents to classify their feedback as good, fair, poor, and bad. Is the study observational or … experimental? If it is an experiment, what is the … factor?
5. In a survey conducted to find out the feedback of a sports program organized in a club, the organizers asked the respondents to … classify their feedback as good, fair, poor, and bad. Is the study observational or experimental? If it is an experiment, what is the … factor?
6. A study was … with a random sample of 513bolts produced at one factory. What population would … appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases?
7. A researcher wants to find out the effect of the amount of protein eaten at breakfast on the aerobic…  performance of runners. Would an experimental or observational study design … more appropriate?
8. In the description of the following experiment, determine the experimental factor. A pharmaceutical company conducted an experiment to test a breakfast drink for school children. The company enrolled students for the experiment in the age group of 6to 10 and divided them into two groups. One group received the … new breakfast drink with their normal breakfast, and the other group drank the same amount of a similar looking juice. Identify the experimental factor.
9. A study was … with a random sample of 200people from one college. What population would … appropriate for generalizing conclusions … from the study, assuming the data collection methods used did not introduce biases?
10. A team of physicians is studying a weight-loss pill. They recruited volunteers for a study. The volunteers were in the age group of 30to 35 and were more than 40 pounds overweight. The physicians gave the … new weight-loss pill pack to one group. The other group received a pill pack that resembled the new weight-loss pill pack but was a placebo. In the description of the above situation, determine the experimental group.
11. A study was conducted among school students on the relationship between getting up late and getting to school late. Is this an example of an observational study or experimental study? If it is an experiment, what is the controlled factor?
12. A consumer research company is interested in … determining if a certain company’s new refrigerator model is more efficient than the older model. What should the researchers do first?
13. A research team is testing a product that will minimize wrinkles among women. Volunteers in the age group of 40to 45 are included in the research. The research team gives a bottle of the solution to one group and a similar …  bottle of solution with no ingredients intended to lessen wrinkles to the other group. In the description of the above situation, determine the control group.
14. Is a survey of the guests about their preference of food at a party an observational study or experimental study? If it is an experiment, what is the … factor?
15. A pharmaceutical company conducted an experiment to test a drug for controlling diabetes. The company enrolled participants for the … experiment and divided them into 2 One group received an inert drug, and the other group received the diabetes-control drug. In the description of the above experiment, determine the control group.
16. A consumer research company is interested in determining if a certain company’s new refrigerator model is more … efficient than the older model. Researchers decide to investigate the claim that the new model uses 10%less electricity than the older model for the same cooling load. Which data collection method is appropriate? Select only one answer choice.
17. In a study to identify the effectiveness of drugs in reducing smoking habits, the study participants were grouped into 3 Each of the groups was … randomly to one type of drug, either Drug A, Drug B, or Drug C. Results were … for a 4 week period. Is the study observational or experimental? If it is an experiment, what is the … factor?
18. A consumer research company is … in determining if a certain company’s new refrigerator model is more efficient than the older model. Which might … an appropriate claim to result from this research?
19. In a psychological study aimed at testing a medicine for reducing stress levels, the researcher grouped the participants into 2groups and …gave a stress-reduction pill to one group and a placebo pill to another group. In the description of the above situation, determine the control group.
20. A candy manufacturer is … in the distribution of colors in each of its packages of candy sold. The manufacturer randomly sample packages from multiple batches at one factory. Are the results generalizable to the company’s other factories that produce the same candy?
21. A biologist is interested in finding the relationship between the amount of sunlight and the growth rate of sunflowers. Would an experimental or observational study design … more appropriate?
22. To test the effectiveness of a drug proposed to relieve symptoms of depression, psychiatrists recruited volunteers for … clinical tests. All of the volunteers were … with symptoms of depression. The psychiatrists provided the drug to first group and a sugar pill to the second group. In the description of the above situation, determine the control group.
23. A scientist is interested in finding … out the effect of soil quality on crop quality. Would an experimental or observational study design … more appropriate?
24. A researcher is … in the effects of watching videos just before bed on the quality of sleep. He has decided to test the claim “Watching 1hour of video just before going to bed reduces the number of minutes of REM sleep by … more than 10%.” How should the number of hours of video … treated?
25. In the description of the following experiment, determine the experimental factor. A team of physicians testing a new liquid drug taken using an inhaler for treating colds gave the drug to one group of volunteers enrolled for … the test. They gave the other group water using the same kind of inhaler.
26. A candy manufacturer is … in the distribution of colors in each of its packages of candy sold. Which question is appropriate for their research?
27. Is an online poll asking the … preferred mobile phone type used by school children an observational study or experimental study? If it is an experiment, what is the … factor?

# MATH 225N Week 1 Assignment Sampling Methods – Questions and Answers

1. Assume that 80houses are present in the form of a grid consisting of 10 columns and 8 If a loudspeaker is placed just before the first row, which sampling method works the best to select a sample of houses if we … want to get an estimate of the average loudness (measured in decibels) near all the 80 houses?
2. Angela is studying the mean blood pressure of all students attending her college. She collects data from the … 38students in her statistics class. Which type of sampling is used?
3. A town planner is interested in getting some demographic data about the households in the city. The city has four wards with the … following numbers of households: ward A has 2,107, ward B has 903, ward C has 1,505, and ward D has 1,499. The budget for the project allows the planner to survey 100 She plans to use a stratified sampling method. What number of households should be chosen from ward B? Enter a whole number.
4. Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into … groups by grade level and randomly selecting a proportionate number of students from each group. He then collects data from the sample. Which type of sampling is used?
5. An executive for a large national restaurant chain with multiple locations in each of 513counties wants to personally sample the … cleanliness of the chain’s restaurants throughout the country by visiting restaurants. The executive wants a good-quality sample but wants to minimize travel time and expenses. Which of the following sampling methods would be most appropriate?
6. considering different sampling methods, stratified sampling includes the steps: _______.
7. When is using a simple random sample appropriate?
8. Ruby is studying the mean waist size of all students attending her college. She collects data from the 25students in her statistics class. Which type of sampling is used?
9. A school district’s superintendent wants to administer a test of life skills to a sample of students. The superintendent has ample time and resources to conduct the study, as well as access to detailed information about all … students’ addresses, courses, grades, and attendance. Which of the following would be the worst sampling method for the superintendent to use?
10. In reference to different sampling methods, cluster sampling includes the steps: use simple random sampling to select a set of groups; every individual in the … chosen groups is included in the sample.
11. A television station plans to send a crew to a polling center on an election day. Because they do not have time to … interview each individual voter, they decide to count voters leaving the polling location and ask every 20th voter for an interview. What type of sampling is this?
12. William is studying the hair colors of all students attending his college. He collects data from the 25students in his … statistics class. Which type of sampling is … ?
13. A manufacturer has three tool centers that each make about 1000tools every day. In order to implement better quality-control procedures, the manager wants to start sampling the tools made each day to be … able to identify issues as quickly as possible. Which sampling method would be most appropriate?
14. To study the eating habits of all athletes in his school, Christopher obtains a list of the athletes and collects data from every 10th person … on the list. Which type of sampling is … ?
15. A grocer receives cartons of 12eggs in boxes of 100 In a particular month, the grocer receives 4 shipments of eggs with 20 boxes in each shipment. The grocer wants to estimate the proportion of … cartons he receives this month that include at least one broken egg. Which of the following sampling methods would be most appropriate?
16. To study the mean head size of all athletes in his school, Kenneth obtains a list of the athletes and collects data from every 6th person … on the list. Which type of sampling is … ?
17. A professor is … in the average length of books in her library. She has divided her books into a few different categories: 235books on mathematics, 290 books on sports, and 166 books on interior design. Rather than … examining all the books, she plans to use a stratified sample of 50 How many of the sports books should she choose? Enter a whole number.
18. Tina is studying the shoe sizes of all students attending her university. She samples the student population by selecting every 18th student from an … alphabetical list of the students. Which type of sampling is … ?
19. The management of a large airline wants to estimate the average time after takeoff taken before the crew begins serving snacks and … beverages on their flights. Assuming that management has easy access to all of the information that would … to select flights by each proposed method, which of the following would be reasonable methods of stratified sampling? Select all that apply.
20. When considering different sampling methods, systematic sampling includes the steps: _______.
21. A television station wants to report on a local election. The station has three crews that can … used during the day … for collecting data. What sampling method would be appropriate?
22. In reference to different sampling methods, systematic sampling includes the steps: list the members of the population; use simple random sampling to select a starting point in the … population; let k= (number of individuals in the population)/(number of individuals needed in the sample); choose every kth individual in the list starting with the one that was randomly …
23. A town planner is … in getting some demographic data about the households in the city. The city has ten wards that … vary in size. Which sampling method is most appropriate?
24. When considering different sampling methods, cluster sampling includes the steps: _______.
25. A quality manager at a manufacturing plant needs to get a sample of widgets for monitoring the manufacturing processes. He plans to choose one out of every Nwidgets produced. The plant makes … about 5100 widgets per day, and the quality team has enough time to examine about 60 widgets each day. What value should the manager use for N? Enter a whole number.5100/60 = 85
26. Cluster sampling includes the steps: divide the population into groups; use simple random sampling to identify a proportionate number of individuals from each group.
27. A quality-assurance worker wants to … systematically sample 120glass jars each day from a conveyor belt in a factory that puts out 3,600 jars each day. If the worker will select every kth jar, what is the best value of k for the worker to use? Enter a whole number.3600/120 = 30
28. In order to study the mean pulse rate of people in his town, Jerry samples the population by dividing the residents by regions and … randomly selecting 12of the regions. He collects data from all

# MATH 225N Week 2 Statistics Quiz – Question and Answers

1. A company has developed a wristband for monitoring blood sugar levels without requiring direct blood samples. It is interested in demonstrating the accuracy of the device for governmental approval and has decided to test … the claim “The glucose level reported by the wristband is within 10%of a standard blood test result.” Which of the following data collection processes would be appropriate? Select only one answer choice.
2. A farmer divided his piece of land into 4equivalent groups. The quality of the soil is the same across the 4 groups of land. He planted the … same crop in all 4 groups of land and recorded the yield of the crop in all 4 groups for a 4 week period. Is the study observational or experimental? If it is an experiment, what is the controlled factor?
3. To test the effectiveness of a drug proposed to relieve symptoms of headache, physicians included participants for a study. They gave the … drug to one group and a drug with no therapeutic effect to another group. Which group receives the placebo?
4. Matthew has created a survey to test whether or not gender has any effect on political party associations. What is the explanatory variable in this situation?
5. Is the statement below true or false?
6. Continuous data are the type of quantitative data that is the result of measuring.
7. A doctor notes her patient’s temperature in degrees Fahrenheit every hour to make sure the patient does not get a fever. What is the level of measurement of the data?
8. Karen wants to estimate the mean number of … siblings for each student in her school. She records the number of siblings for each of 200randomly selected students in the school. What is the sample?
9. True or False? In reference to different sampling methods, systematic sampling includes the steps: divide the population into … groups; use simple random sampling to identify a proportionate number of individuals … from each group.
10. While standing on a highway overpass, Jennifer wonders what proportion of the vehicles that pass on the highway below are trucks. The highway has 4lanes running in each direction. Jennifer is only interested in the … proportion of … vehicles that pass over the course of the hour that she spends there. Which of the following sampling methods would be best for Jennifer to employ?
11. As a member of a marketing team, you have been tasked with determining the number of DVDs that people have rented over the past six months. You sample twenty adults and decide that the best display of data is a frequency table … for grouped data. Construct this table using four classes.
12. The values and relative frequencies for a set of data are shown below. Complete the cumulative relative frequency table.
13. The histogram below displays the … weights of rainbow trout (in pounds) caught by all visitors at a lake on a Saturday afternoon. According to this histogram, which range of weights (in pounds) contains the lowest frequency?
14. Describe the shape of the given histogram.
15. A set of data is … by the stem and leaf plot below.
16. The bar graph below shows the number of boys and girls in different classes.
17. The line graph shown below represents the number of TVs in a house by … square footage (in hundreds of feet). According to the information above, which of the following is an appropriate analysis of square footage and TVs?
18. Ashley is reviewing past monthly credit card statements.  The statements are … in the relative frequency table below.
19. What is the cumulative relative frequency of credit card statements that are \$1245 or less?
20. The bar graph below shows the number of men and women in different clubs.
21. An English professor asks her students who their favorite character is in the novel they are reading. What is the level of measurement of the data?
22. Jessica is keeping track of her favorite stock’s price. The line graph below shows the data.
23. A set of data is … by the stem and leaf plot below.
24. Describe the shape of the given histogram.
25. A data set is … in the frequency table below. Using the table, determine the number of occurrences of values greater than or equal to
26. Give your answer as a single number. For example, if you found the number of values was 23, you would enter 23.
27. Timothy wants to estimate the mean number of siblings for each student in his school. He records the number of siblings for each of 75 randomly selected students in the school. What is the statistic?
28. In a psychological study aimed at testing a drug that reduces anxiety, the researcher grouped the participants into 2groups and gave the … anxiety-reduction pill to one group and an inert pill to another group. Which group receives the placebo?

# MATH 225N Week 2 Discussion, Graphing and Describing Data in Everyday Life

Suppose that you have two sets of data to work with. The first set is a list of all the injuries that were seen in a clinic in a month’s time. The second set … contains data on the number of minutes that each patient spent in the waiting room of a doctor’s office. You can make assumptions about other information or variables that are included in each data set.

For each data set, propose your idea of how best to represent the key information. To organize your data would you choose to use a frequency table, a cumulative frequency … table, or a relative frequency table? Why?

What type of graph would you use to display the organized data … from each frequency distribution? What would be shown on each of the axes for each graph?

# MATH 225N Week 2 Assignment, Frequency Tables Question and Answers

1. A data set is … in the frequency table below. Using the table, determine the number of values less than or equal to 5. Give your answer … as a single number. For example if you found the number of values was 19, you would enter 19.
2. Given the frequency table, how many times does the data value 3show up in the data set?
3. A group of students were … about the number of siblings they have. The frequencies and relative frequencies of their responses are … in the below. Complete the cumulative relative … frequency table.
4. Given the relative frequency table below, which of the following is the corresponding cumulative relative frequency table?
5. A group of students were … about the number of books they read last summer. Their responses are … in the frequency table below. How many students responded to the survey?
6. The ages of the students in an art class at the community center are … below.  9,11,14,14,16,21,24,26,32,33,37,38,38,52,53,55. Complete the frequency table.1,4,3,5,0,3
7. A data set is … in the frequency table below. Using the table, determine the number of values less than or equal to 7in the data set. Give your answer as a single number. For example if you found the number of … values was 16, you would enter 16.
8. A data set is … in the frequency table below. Using the table, determine the number of values less than or equal to 6. Give your answer as a single number. For example if you found the number of values was 14, you would enter 14.
9. As the manager of a store, you wish to determine the amount of money that people who visit this store are willing to spend on impulse buys on products placed near the checkout register. You sample twenty individuals and records their responses. Construct a frequency table for grouped data using five classes.  8,18,15,10,29,4,15,2,4,9,16,14,13,8,25,25,27,1,15,24
10. As a member of a marketing team, you have been … with determining the number of DVDs that people have rented over the past six months. Their responses are … in the relative frequency table below. What is the cumulative relative frequency of customers who rent 27 or fewer DVDs?
11. Given the relative frequency table below, which of the following is the corresponding cumulative relative frequency table?
12. Several executives were … how many suits they own.  The results are … in the … frequency table.
13. Describe the shape of the given histogram.
14. Several people were … to report the number of hours of sleep they average per night.  The results are … in the histogram below.  How many of those people average between 5and 6.5 hours of sleep per night?
15. Describe the shape of the given histogram.
16. The histogram below represents the … prices of digital SLR camera models at a store. Describe the shape of the distribution.
17. Given the following histogram for a set of data, how many values in the data set are between 5 and 8.5?
18. Describe the shape of the given histogram.
19. A professor gave students a test, and the distribution of the scores of the students is shown in the histogram below. What shape does the distribution have?
20. The author of a book wants to know what price his book is being sold for. He gets the price from all the bookstores in a city and creates a histogram of the results. What is the shape of the distribution?
21. Given the following histogram for a set of data, how many values in the data set are between 5and 9.5?
22. Gail is a car salesperson, who keeps track of her sales over time. The line graph below shows the data for the number of cars she sells per week.
23. Porter is keeping track of the total number of books he has read over time. The line graph below shows the data.
24. The bar graph below shows the number of men and women in different classes.
25. The bar graph below shows the number of men and women in different classes.
26. An accounting manager is conducting research on how many times each accountant in the office checks their work. The following table shows the number of times each accountant checks their work.
27. The accounting manager encourages accountants to check their work at least two times to ensure there are no calculation errors. According to the data above, should the accounting manager … concerned about errors made in the work conducted at the office?
28. Jackie invited her friends over for a movie night. She asked each of her friends to come over about their favorite movie snack. The following table shows the favorite movie snacks of her friends.
29. If Jackie can only get two movie snacks for a movie night with her friends, which two movie snacks should she purchase?
30. Marc is keeping track of the total number of movies he has watched over time. The line graph below shows the data where the number of movies corresponds to the number of movies that had been watched at the beginning of the … week shown on the horizontal axis.
31. Josslyn is a car salesperson who keeps track of her sales over time. The line graph below shows how many cars she sells per week.
32. A set of data is … by the stem and leaf plot below.
33. A set of data is summarized by the stem and leaf plot below.
34. A set of data is … by the stem and leaf plot below…

# MATH 225N Week 3 Lab Assignment, Frequency Distribution – Neonates and Weight Loss

Steps to Complete Week 3 Lab

Step 1: Go to the Chamberlain Library at: https://library.chamberlain.edu (Links to an external site.).

Step 2: Click Databases in the Search the Library block. Then choose ProQuest Nursing and Allied Health Database in the dropdown menu.

Database Search Example

Step 3: Below, you will find the titles of six articles from the ProQuest database that show a frequency distribution within the article. CHOOSE ONE OF THE ARTICLES FROM THE LIST BELOW. You will perform two searches using this article.

(1) For our first broad-based search, use the underlined words in your chosen article to search and see how many articles from the database contain these underlined words (see the example below the article list for an example search on post-partum depression).

Article Titles

1. Oral manifestations in diabetic patients under treatment for ischemic heart diseases: A comparative observational study
2. Systolic blood pressure, diastolic blood pressure, and pulse pressure: An evaluation of their joint effect on mortality
3. The Relationship Between Body Mass Index (BMI) and Menstrual Disorders at Different Ages of Menarche and Sex Hormones
4. Adolescents’ first tobacco products: Associations with current multiple tobacco product use
5. Association of lifestyle modification and pharmacological adherence on blood pressure control among patients with hypertension at Kenyatta National Hospital, Kenya: A cross-sectional study
6. Demographic, parental, and personal factors and youth athletes’ concussion -related knowledge and beliefs

Example of search on post-partum depression

Make sure to checkmark Full Text and Peer Reviewed, and choose Last 12 Months from the drop-down list. Also, choose English under the language section.

This will yield a list of articles about the topic that you chose. Look to see how many results were found.

(2) For our second more narrow search, go back and search for the title of the article that you chose originally. Type A PORTION of the article title into the search bar and find the full PDF for that article. ‘

Step 4: Complete your lab by taking the following steps

1. Copy and paste, or post a screen shot of the frequency distribution from the article you chose at the top of your Word document.
1. On your first search, what terms did you use, and what other things did you mark on the search page before conducting your search? Why did you choose the article that you did? How many articles were found with these search terms? Give the full APA reference of the article you are using for this lab.
1. What data are shown in the frequency distribution and why might it be of interest? Include the size of the classes, noting if they are of a consistent size or not. Also include a conclusion that could be made from the frequency distribution. (1 to 2 paragraphs)
1. How else might these data have been displayed? Discuss pros and cons of 2 other presentation options, such as tables or different graphical displays (1 to 2 paragraphs)

Step 5: Be sure your name is on the Word document, save it, and then submit it under “Assignments” and “Week 3: Lab”.

# MATH 225N Week 3 Central Tendency Questions and Answers

1. Given the following box-and-whisker plot, decide if the data is skewed or symmetrical.
2. Which of the following frequency tables show a skewed data set? Select all answers that apply.
3. Which of the following frequency tables show a skewed data set? Select all answers that apply.
4. Which of the following frequency tables shows a skewed data set? Select all answers that apply.
5. For the following dataset, you are interested to determine the “spread” of the data……Would you employ calculations for the sample standard deviation, or population standard deviation for this data set: Ages of all students in a Statistics course with an enrollment of 30 students.
6. Which of the data sets represented by the following histograms has the smallest standard deviation?
7. A company is interested to know the variation in … yearly sales amount for all 5 salespeople in the company.
8. Which of the data sets represented by the following histograms has the smallest standard deviation?
9. The data set shown below is the … sales amount sold by the 5 salespeople in the company (expressed in thousands of dollars): 40,60,65,70,80 ….. Find the variance for this dataset.
10. The data below are the monthly average high temperatures for November, December, January, and February in New York City from the Country Studies/Area Handbook Series sponsored by the U.S. Department of the Army between 1986 and 1998. What is the sample standard deviation? …..54,42,40,40…….Round the final answer to one decimal place.
11. The following data values represent the daily amount spent by a family during a 7 day summer vacation. Find the sample standard deviation of this … dataset: \$96, \$125, \$80, \$110, \$75, \$100, \$121….
12. Round the final answer to one decimal place.
13. Which of the following lists of data has the smallest standard deviation?
14. Which of the following lists of data has the smallest standard deviation?
15. Find the median of the following set of miles per gallon for randomly selected sports cars…..36,22,24,30,44,13,21,34,18
16. Find the mode of the following number of times each machine in a car factory needed to be fixed within the last year…..2,5,6,12,14,12,6,2,5,3,14,5
17. Laura runs at the park after school and wants to know the mean number of miles she runs. The numbers for the … miles run each day so far are listed below……8,9,7,13,3,9,14…….Find the mean number of miles she runs daily.
18. An art collector bought 20paintings at an art fair, and wants to know the average price of her new paintings. She adds the prices of all the paintings and divides this number by 20 to find an average price of \$350 . Is this price a sample mean or a population mean, and which symbol would be used to denote it?
19. Given the following list of the … number of pens randomly selected students purchased in the last semester, find the median…..13,7,8,37,32,19,17,32,12,26
20. Find the mode of the following amounts of exercise (in hours) randomly selected runners completed during a weekend……2,14,14,4,2,4,1,14,4,4,8
21. Find the mode of the following list of points earned on a 16 point quiz given during a finance class. 7,7,3,2,7,16,12,16,12
22. Find the median of the following set of data. 35,43,18,35,29,27,19,19…….Give your answer as a number only. For example, if you found the median was 34, you would enter 34.
23. Each person in a group shuffles a deck of cards and keeps selecting a card until an ace appears. Find the mode of the following number of cards drawn from a deck until an ace appears. 14,10,7,14,9,9,10,12,9,7,12
24. A grandfather wants to know the average height of all his grandchildren. He finds that the heights of his 9grandchildren are given in inches by…63,71,60,59,74,60,60,75,58.
25. What is the population mean of the height of his grandchildren in inches? Round your answer to the nearest tenth of an inch and do not include units.
26. Given the following list of the number of pencils randomly selected students used in a school year, find the median…..10,22,6,7,19,5,27
27. A teacher randomly selects 10out of her 30 students and finds that the mean height of those 10 students is 5′2″. Is this a sample mean or a population mean, and which symbol would be used to denote it?
28. A data set lists the number of strikes scored per team during a bowling league championship. For this data set, the minimum is 2, the first quartile is 3, the median is 5, the third quartile is 7, and the maximum is 14. Construct a box-and-whisker plot that shows the number of strikes scored.
29. Given the following frequency table of data, what is the potential outlier?
30. Given the following frequency table of data, what is the potential outlier?
31. A data set lists the number of extra credit points awarded on midterm scores of 15students taking a statistics course. For this data set, the minimum is 3, the median is 15, the … third quartile is 16, the interquartile range is 4, and the maximum is 19. Construct a box-and-whisker plot that shows the extra credit points awarded.
32. Given the following list of data, what is the five-number summary? 10, 12, 14, 14, 14, 16, 17, 17, 17, 19, 19
33. The following frequency table summarizes a set of data. What is the five-number summary?
34. The following frequency table summarizes a set of data. What is the five-number summary?
35. The following frequency table summarizes a set of data. What is the five-number summary?
36. Given the following frequency table of data, what is the potential outlier?
37. The five number summary for a set of data is given below. What is the interquartile range of the set of data? Enter just the … number as your answer. For example, if you found that the interquartile range was 25, you would enter 25.
38. The five number summary for a set of data is given below. Using the interquartile range, which of the following are outliers? Select all correct answers.
39. Given the following frequency table of data, what is the potential outlier?
40. The five number summary for a set of data is given below….. What is the interquartile range of the set of data?
41. The five number summary for a set of data is given below……Using the interquartile range, which of the following are outliers? Select all correct answers.
42. A data set lists the number of hours each student, from a finance class, studied for a midterm. For this data set, the … minimum is 3, the median is 6, the third quartile is 9, the interquartile range is 5, and the maximum is 17. Construct a box-and-whisker plot that shows the number of hours studied. Begin by first placing the middle dot on the median. Then work on placing the rest of the points starting with the ones closest to the median.
43. A data set lists the number of hours waiters worked at a restaurant every Friday during the last year. For this data set, the minimum is 1, the median is 5, the third quartile is 8, the interquartile range is 4, and the maximum is 17. Construct a box-and-whisker plot that shows the number of hours worked on a Friday.
44. The following dataset represents the favorite color reported by young children at a birthday party: Blue, Green, Red, Blue, Blue, Yellow, Pink, Yellow, Red, Red, Blue, Blue, Blue, Green, Blue……Which of the following would be best to describe a typical value in the dataset?
45. The following histogram shows the monthly rents reported in a survey of university students. Which of the following would be a reasonable measure of central tendency for this dataset? Select all that apply.
46. The following dataset represents the dollar amounts of donations collected at the entrance to a free museum during one hour…….. Is the median a reasonably good measure of central tendency for this dataset? What if the outlier were removed from consideration?
47. The following dataset represents the math test scores for a class of 20students…..              90, 60, 85, 100, 100, 90, 100, 75, 100, 95, 95, 85, 30, 100, 40, 15, 100, 90, 70, 80…….. Identify the best measure of central tendency for this dataset.
48. The following is a dataset of salaries for a company (in thousands).  Find the mean and median and determine if the mean or … median is the better measure of central tendency…..11,87,85,95,92,93,97
49. The following dataset represents the math test scores for a class of 20students…….              90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75…..Would the mode be a good measure of central tendency for this dataset?
50. The following histogram shows menu prices of entrees at a local restaurant. Identify the best measure of central tendency for this dataset
51. The following dataset represents the math test scores for a class of 20students……       90, 85, 95, 100, 100, 90, 100, 70, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75…… How many outliers are in this dataset?
52. A trainer would like to find the mean number of sports drinks the people in her class had in the last week. She collects data from 26participants in her aerobics class. The graph shows the frequency for the … number of sports drinks……..Find the mean number of sports drinks consumed by the 26 participants, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.
53. A student at a fashion school would like to find the mean number of hats his fellow students own. He collects data from 25students in his fashion design course. The graph shows the frequency for the number of hats owned by his fellow classmates……Find the mean number of hats owned by the 25students, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.
54. Given the frequency table below, which equation shows the mean of the set of data?
55. For the grouped frequency table shown below which shows salaries at a company (expressed in thousands), find the … midpoint for the second row in the table:
56. Given the frequency table below, what is the estimated mean? Round your answer to two decimal places.
57. A manager at a shoe factory would like to find the mean number of breaks taken by employees on a particular Friday. He collects data from 15fellow coworkers in the factory. The graph shows the frequency for the number of breaks taken during this time period…….Find the mean number of breaks for the 15 coworkers, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.
58. A student would like to find the mean number of people living in households in a neighborhood. She collects data from 65homes in the area. The graph shows the frequency for the number of people living in the homes.
59. Find the mean number of people living in the 65homes, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean…….A student would like to find the mean number of people living in households in a neighborhood. She collects data from 65homes in the area. The graph shows the frequency for the number of people living in the homes…….Find the mean number of people living in the 65 homes, and round … your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.
60. Find the mode of the following amounts (in thousands of dollars) in checking accounts of randomly selected people aged 20-25……2,4,4,7,2,9,9,2,4,4,11
61. Find the mode of the following number of states randomly selected travelers at a service plaza visited in the past three years…….18,13,8,8,13,10,13,10,9,18
62. The following is a dataset of the average weekly number of cups of coffee consumed by employees in an office. Find the mean and … median and determine if the mean or median is the better measure of central tendency…….5,0,5,2,0,10,7,8,10,21,5,8,2,5,3,5
63. The following histogram shows the dollar amounts of donations collected by a charitable organization over the course of a month. Identify the best measure of central tendency for this dataset.
64. The following dataset represents the math test scores for a class of 20students……90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75…..Suppose that the last value, 75, was mistakenly recorded as 5. What measure(s) of the typical value in a dataset would be … affected by this error? Select all that apply.

# MATH 225N Week 3 Discussion, Central Tendency and Variation

Understanding descriptive statistics, their measures of center and their variability helps form the foundation of statistical analysis. Descriptive statistics tell us how frequently an observation occurs, what is considered average, and how far … data in our sample deviate from being average. With these statistics, we are able to provide a summary of characteristics from both large and small datasets. Measures of central tendency and … variability provide valuable information on their own, and form the cornerstone of the quantitative structures that we build in our research studies…

For this Discussion, you will examine central tendency and variability in terms of pulse rate.

Find and record the pulse rate of 10 different people where you work. Tell us a little about the population … from which you drew your data. Describe your findings in terms of central tendency and variability. Consider using some of the following to help you form your initial discussion post:

• What are your measures of central tendency (i.e., mean, median, and mode)? Which might be the better measure for … central tendency and why?
• What is the standard deviation of your data? How variable are the data (range)?
• Are there any outliers? Investigate possible … reasons for these outliers, and things that might limit them if further study were to be carried out. What are some variables that should be … in discussing your measures of central tendency and variation? Is there any skewness in your … data?
• How would you describe this data (i.e. what insights did you gain from this data)?

# MATH 225N Week 4 Homework Probability Question and Answers

1. Which of the pairs of events below is dependent?
2. Identify the option below that represents dependent events.
3. … shows mutually exclusive events?
4. Which of the pairs of events below is mutually exclusive?
5. A deck of cards contains RED cards numbered 1,2,3,4,5,6, BLUE cards numbered 1,2,3,4,5, and GREEN cards numbered 1,2,3,4. If a single card is … at random, what is the probability that the card has an ODD number?
6. Hector is a baseball fan but wants to watch something different. There are 5basketball games, 2 football games, and … 4hockey games that he can choose to watch. If Hector randomly chooses a game, what is the probability that it is a basketball game?
7. There are 26cards in a hat, each of them containing a different letter of the alphabet. If one card is … at random, what is the … probability that it is not between the letters L and P, inclusive?
8. A spinner contains the numbers 1through 80. What is the probability that the spinner will land on a number that is not a multiple of 12?
9. An art collector wants to purchase a new piece of art. She is … in 5paintings, 6 vases, and 2 If she … the piece at random, what is the probability that she … a painting?
10. Boris is taking a quiz for an online class. For the quiz, the system randomly assigns 2high-difficulty questions, 7 moderate-difficulty questions, and 6 low-difficulty questions. What is the probability that … Boris is assigned a moderate-difficulty question first?
11. A spinner contains the numbers 1through 40. What is the probability that the spinner will land on a number that is not a multiple of 6? Give your answer as a fraction.
12. A spinner contains the numbers 1through 50. What is the probability that the spinner will land on a number that is not a multiple of 4?
13. Identify the parameters pand n in the following binomial distribution scenario. The probability of winning an arcade game is 718 and … the probability of losing is 0.282. If you play the arcade game 20 times, we want to know the probability of winning more than 15 times. (Consider winning as a success in the binomial distribution.)
14. A weighted coin has a 55probability of landing on heads. If you toss the coin 14 times, what is the probability of … getting heads exactly 9 times? (Round your answer to 3 decimal places if necessary.)
15. Identify the parameter pin the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 546 and without a popcorn coupon is 0.454. If you buy 27 movie tickets, we want to know the … probability that exactly 15 of the tickets have popcorn coupons. (Consider tickets with popcorn coupons as successes in the binomial distribution.)
16. A softball pitcher has a 64probability of throwing a strike for each pitch. If the softball pitcher throws 20 pitches, what is the probability that exactly 13 of them are strikes?
17. Identify the parameter nin the following binomial distribution scenario. A basketball player has a 429 probability of making a free throw and a 0.571 probability of missing. If the player shoots 20 free throws, we want to know the probability that he makes no more than 12 of them. (Consider made free throws as successes in the binomial distribution.)
18. Give the numerical value of the parameter pin the following binomial distribution scenario…..A softball pitcher has a 675 probability of throwing a strike for each pitch and a 0.325 probability of throwing a ball. If the softball pitcher throws 29 pitches, we want to know the probability that exactly 19 of them are strikes……..Consider strikes as successes in the binomial distribution. Do not … include p= in your answer.
19. Identify the parameters pand n in the following binomial distribution scenario……Jack, a bowler, has a 38 probability of throwing a strike and a 0.62 probability of not throwing a strike. Jack bowls 20times (Consider that throwing a strike is a success.)…….The Stomping Elephants volleyball team plays 30 matches in a week-long tournament. On average, they win 4 out of every 6matches. What is the mean for the … number of matches that they win in the tournament?
20. Using the same scenario, what is the standard deviation for the number of matches that they win in the tournament?
21. The Stomping Elephants volleyball team plays 30matches in a week-long tournament. On average, they win 4 out of every 6
22. Identify the parameter nin the following binomial distribution scenario. A weighted coin has a 441 probability of landing on heads and a … 0.559 probability of landing on tails. If you toss the coin 19 times, we want to know the probability of getting heads more than 5 times. (Consider a toss of heads as success in the binomial distribution.)
23. Give the numerical value of the parameter n, the number of trials, in the following binomial distribution scenario.
24. A weighted coin has a 486probability of landing on heads and a 0.514 probability of landing on tails. If you toss the coin 27 times, we want to know the probability of getting heads exactly 11 times.
25. Consider a toss of heads as success in the binomial distribution.
26. The probability of winning on an arcade game is 659. If you play the arcade game 30times, what is the probability of winning exactly 21 times?
27. The probability of buying a movie ticket with a popcorn coupon is 526. If you buy 26movie tickets, what is the probability that exactly 15 of the tickets have popcorn coupons?
28. The probability of buying a movie … ticket with a popcorn coupon is 608. If you buy 10movie tickets, what is the probability that more than 3 of the tickets have popcorn coupons? (Round your answer to 3 decimal places if necessary.)
29. A softball pitcher has a 507probability of throwing a strike for each pitch. If the softball pitcher throws 15 pitches, what is the probability that … more than 8 of them are strikes? (Round your answer to 3 decimal places if necessary.)
30. A 2014 study by researchers at the University College Antwerp and the University of Leuven showed that e-cigarettes are effective at reducing cigarette craving.  Participants were separated into two groups. One group was … e-cigarettes and the other was told to not smoke e-cigarettes. Two months later, researchers observed how many participants had … stopped smoking cigarettes……..The following table shows approximate numbers. According to the table, what is the probability that a randomly … participant did not stop smoking, … that the participant received an e-cigarette?
31. Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 The data are … in the contingency table below. What is the relative risk of flying for those birds that have long beaks? … decimal places.
32. Given the contingency table below, determine the marginal distribution of breakfast and lunch. Round your answer(s) to the nearest whole number. Select all that apply.
33. 155fitness center members were asked … if they run and if they lift weights. The results are … in the table below……. Given that a randomly selected survey participant does not run, what is the probability that the participant lifts weights?
34. Fill in the following contingency table and find the number of students who both have a cat AND have a dog.
35. Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 The data are … in the contingency table below. What is the odds ratio for birds that fly having long beaks against birds that do not … fly having long beaks? Round your answer to two decimal places…….. Fill in the following contingency table and find the number of students who both watch comedies AND watch dramas.
36. Researchers wanted to study if couples having children are married. They surveyed a large group of people. The data are … in the contingency table below. What is the odds ratio for married people having children against unmarried people having children? Round your answer … to two decimal places.
37. Doctors are testing a new antidepressant. A group of patients, all with similar characteristics, take part in the study. Some of the patients receive the new drug, while others receive the traditional drug. During the study, a number of patients complain about insomnia. The data are … in the contingency table below. What is the … relative risk of insomnia for those who receive the new drug? Round to two decimal places.
38. A group of college freshman are targeted with a voter registration advertisement. Another group of freshman are not targeted. The table below shows how many of these freshman registered to vote. What is the odds ratio for freshman targeted with the advertisement registering to vote against freshman not targeted with the advertisement registering to vote? Does the advertisement appear to have been successful? Round to … two decimal places.
39. Researchers … to depression. They surveyed a large group of people. The data are … in the contingency table below. What is the relative risk of … ? Round your answer to two decimal places.
40. Researchers want to study whether or not a fear of flying is related to a fear of heights. They surveyed a large group of people and asked … them whether or not they had a fear of flying and whether or not they had a fear of heights. The data are … in the contingency table below. What is the relative risk of being afraid of flying for those who are afraid of heights? Round your answer to two decimal places.
41. A study of drivers with speeding violations in the last year and drivers who use cell phones produced the following fictional data: ………. Find the probability that a randomly chosen person takes public transit to work given that the person does not support the environmental bill…
42. Fill in the following contingency table and find the number of students who both do not go to the beach AND do not go to the mountains.
43. Fill in the following contingency table and find the number of students who both have a cat AND have a dog.
44. Researchers wanted to study if couples having children are married. They surveyed a large group of people. The data are … in the contingency table below. What is the odds ratio for people having children to … married against … people not having children to … married? Round your answer to two decimal places.
45. Researchers wanted to study if wearing cotton clothes is related to depression. They surveyed a large group of people. The data are … in the contingency table below. What is the odds ratio for people wearing cotton clothes being depressed against people not wearing cotton clothes … depressed? Round your answer to two decimal places.
46. Review the flu vaccine data below. What is the odds ratio of not catching the flu for those who receive the new vaccine?
47. Doctors are testing a new antidepressant. A group of patients, all with similar characteristics, take part in the study. Some of the … patients receive the new drug, while others receive the traditional drug. During the study, a number of patients complain about insomnia. The data are … in the contingency table below. What is the relative risk of insomnia for those who receive the new drug? Round to two decimal places.
48. In a recent survey, a group of people were asked if they were happy or unhappy with the state of the country. The data are … in the contingency table below, organized by political party. What is the odds ratio for people unhappy with the … state of the country to be republicans against people happy with the state of the country to … republicans? … two decimal places.
49. Researchers wanted to study if couples having children are married. They surveyed a large group of people. The data are … in the contingency table below. What is the relative risk of being married for those who have children? Round your answer to two decimal places.
50. Kelsey, a basketball player, hits 3-point shots … on 1%of her attempts. If she takes 14 attempts at 3-point shots in a game, what is the probability that she hits exactly six of them? Use Excel to find the probability.
51. A computer graphics card manufacturer is testing an improvement to its production process. If a sample of 100graphics cards manufactured using the new process has a less than 10% chance of having 3 or more defective graphics cards, then the manufacturer will switch to the new process. Otherwise, the manufacturer will stay with its existing process. If the probability of a defective graphics card using the new process is 9%, will the manufacturer switch to the new production process?
52. In a large city’s recent mayoral election, 126,519out of 283,143 registered voters actually turned out to vote. If 20registered voters are randomly selected, find the probability that exactly 8 of them voted in the mayoral election. Use Excel to find the probability.
53. Alex wants to test the reliability of “lie detector tests,” or polygraph tests. He performs a polygraph test on a random sample of 12 If there is more than a 50%chance that the tests result in no false positives (that is, the test does not result in a true statement being recorded as a lie), Alex will conclude that the tests are reliable. If the probability of a lie detector test resulting in a false positive is 5.5%, what will Alex conclude? Use Excel to find the probability, rounding to three decimal places.
54. A certain cold remedy has an 88%rate of success of reducing symptoms within 24 Find the probability that in a random sample of 45 people who took the … remedy, 40 of them had a reduction of symptoms within a day.
55. Kevin works for a company that manufactures solar panels. In a large batch of solar panels, about 1in 200 is defective. Suppose that Kevin selects a random sample of six solar panels from this batch. What is the probability that none of the … solar panels are defective? Use Excel to find the probability.
56. A database system assigns a 32-character ID to each record, where each character is either a number from 0to 9 or a letter from A to F. Assume that each number or letter … is equally … Find the probability that at least 20characters in the ID are numbers. Use Excel to find the probability.
57. A fair spinner contains the numbers 1, 2, 3, 4, and 5. For an experiment, the spinner will … spun 5 If Event A = the spinner lands on numbers all less than 3, what is an outcome of Event A?
58. A poll is conducted to determine if political party has any association with whether a person is for or against a certain bill. In the poll, 214out of 432 Democrats and 246 out of 421 Republicans are in favor of the bill. Assuming political party has no association, the probability of these results being by chance is calculated to … 01. Interpret the results of the calculation.
59. Arianna will roll a standard die 10times in which she will record the value of each roll. What is a trial of this experiment?
60. A health survey determined the mean weight of a sample of 762men between the ages of 26 and 31 to … 173 pounds, while the mean weight of a sample of 1,561 men between the ages of 67 and 72 was 162 The difference between the … mean weights is significant at the 0.05 level. Determine the meaning of this significance level.
61. The mean body temperature of a human is … 6∘F. In a study, the body temperatures of 127individuals were … The mean body temperature of the individuals was … 99.0∘F. Assuming the regular body temperature of humans is actually 98.6∘F, the probability of these results occurring by chance is less than 0.01. Interpret the results of the calculation.
62. Which of the following events seem like they would … unlikely to occur by chance?
63. Before a college professor gave an exam, he held a review session, where 30of his 150 students attended the review. The mean score of the students who attended was 86%, whereas the mean score of the students who didn’t attend the review was 79%. The difference in the mean scores is significant at the 05 level, assuming the review session does not associate with a higher exam score. Determine the meaning of this significance level.
64. According to a recent poll, 5%of people aged 25 years or older in the state of Massachusetts have a bachelor’s degree or higher. The poll also reported that 30.0% of people aged 25 years or older in the state of Delaware have a bachelor’s degree or higher. The poll sampled 354 residents of Massachusetts and 210 residents of Delaware. The data was … at the 0.013 level. Determine the meaning of this significance level.
65. A survey was … to see whether age has an association with the belief that a master’s degree or higher provides an advantage in one’s career. Of the … 524adults between the ages of 22 and 25 surveyed, 56% believed that a master’s degree has value in a person’s career path. Of the 458 adults surveyed between the ages of 40 and 45, 52% also believed that a master’s degree has value in a person’s career path. Assuming age is not … with this belief, the probability of the data being the result of chance is … 21. Interpret this calculation.
66. A farmer claims that the average mass of an apple grown in his orchard is 100g. To test this claim, he measures the mass of 150apples that are … in his orchard and determines the average mass per apple to … 98g. The results are … at the 01 level. What is the correct interpretation of this calculation?
67. Paul will roll two standard dice simultaneously. If Event A = both dice are odd and Event B = at least one die is even, which of the … following best describes events A and B?
68. Patricia will draw 8cards from a standard 52-card deck with replacement. Which of the following are not events in this experiment?
69. Which of the following gives the definition of event?
70. Which of the following gives the definition of trial?
71. Beth is performing an experiment to check if a die is fair. She rolls the die 5times and records the sequence of numbers she gets.
72. Which of the following pairs of events are independent?
73. Is the statement below true or false?…………. Mutually exclusive is the property of events in which none can occur at the same time.
74. Trial best fits which of the following descriptions?
75. Jacqueline will spin a fair spinner with the … numbers 0, 1, 2, 3, and 4a total of 3 If Event A = spinner lands on numbers all greater than … 2 and Event B = total sum of 9, which of the following best describes events A and B.

# MATH 225N Week 4 Discussion, Probability

Consider when you are listening to a new patient who says they have had a fever for 3 days. You would use your knowledge and experience … with probability to come to a diagnosis. What changes those probabilities? Is it age, is it other symptoms, is it new study results? What is the source of these probabilities and what causes these … probabilities to change? This discussion is not to debate diagnoses, but to focus on the sources and influences on probabilities.

# MATH 255N Week 4 Statistics Quiz with Answers

1. Alice sells boxes of candy at the baseball game and wants to know the mean number of boxes she sells. The numbers for the games so far are 16,14,14,21,15……….
2. Given the following list of prices (in thousands of dollars) of randomly selected trucks at a car dealership, find the median…… 20,46,19,14,42,26,33
3. Each person in a group shuffles a deck of cards and keeps selecting a card until a queen appears. Find the mode of the … following number of cards drawn from a deck until a queen appears……. 3,12,3,11,5,5,3,10,12
4. The dataset below represents bugs found by a software tester in her … product during different phases of testing:…..  88, 84, 81, 94, 91, 98, 98, 200. The measures of central tendency are … below: Mean: 25; Median: 92.5; Mode: 98. Identify the outlier and the measure of central tendency that is … by the outlier.
5. Given the following histogram, decide if the data is … or symmetrical…….   A bar graph has a horizontal axis titled Values labeled from 2 to 18 in … increments of 2 and a vertical axis titled Frequency labeled from 0 to 200 in increments of 50. 14 bars are plotted, above the numbers 2 to 16. From left to right, the heights of the bars are as follows: 1. 5. 10. 40, 75, 125, 190, 180, 130, 125, 60, 25,20, 10. All values are approximate.
6. The following data set represents the ages of all seven grandchildren in a family……. 4, 5, 11, 12, 11, 8, 5  If the variance of the ages is 7, what is the … standard deviation? Round the final answer to one decimal place.
7. Which of the data sets represented by the following box and whisker plots has the smallest standard deviation?……. Four horizontal box-and-whisker plots share a … vertical axis with the classes D, C, B, and A and a horizontal axis from 0 to 120 in increments of 20. The box-and-whisker plot above the class label A has the following five-number summary: 44, 69, 77, 82, and 112. The box-and-whisker plot above the class label B has the following five-number summary: 19, 64, 78, 87, and 121. The box-and-whisker plot above the class label C has the following five-number summary: 60, 72, 75, 80, and 92. The box-and-whisker plot above the class label D has the following five-number summary: 2, 63, 77, 92, and 138. All values are approximate.
8. The box-and-whisker plot shows the number of books read by history students during the last school year…… A box and whisker plot with minimum 4, first quartile 6, median 8, third quartile 10, and maximum 15……  What is the range of the data?
9. A random sample of house sizes in major city has a sample mean of x¯=1204.9sq ft and sample standard deviation of s=124.6 sq ft.  Use the Empirical Rule to determine the approximate percentage of house sizes that lie between 7and 1454.1 sq ft…….  Round your answer to the nearest whole number (percent).
10. Is the statement below true or false?….. Independent is the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs.
11. Brayden tosses a coin 500 Of those 500times, he observes heads a total of 416 times. Calculations show that the probability of this occurring by chance is less than 0.01, assuming the coin is fair. Determine the meaning of the …. significance level.
12. A spinner contains the numbers 1through 80. What is the probability that the spinner will land on a number that is not a multiple of 11?….. Give your answer in fraction form.
13. Of the following pairs of events, which pair has mutually exclusive events?
14. Fill in the following contingency table and … find the number of students who both go to the beach AND go to the mountains.
15. A group of 140students at an elementary school were asked if they prefer the color orange to the color green. The results are shown in the table below. Given that a randomly selected survey participant is a male, what is the probability that this student prefers the color green?…… Enter your answer as a fraction.
16. Researchers want to study whether or not a fear of flying is related to a fear of heights. They surveyed a large group of people and asked … them whether or not they had a fear of flying and whether or not they had a fear of heights. The data are … in the contingency table below. What is the relative risk of being afraid of heights for those who are afraid of flying? Round your answer to two decimal places.
17. Which of the following frequency tables show a skewed data set? Select all answers that apply.
18. A student wants to know his average homework grade for the first half of his math class. There were 7homeworks in the first half of the class, and his …. grades out of 100are given by….. 100,90,95,89,92,85,95…… What is the population mean of his homework grades? Round your answer to the nearest tenth.
19. The following data set represents the ages of all six grandchildren in a family….. Find the variance for this data set of ages:….. 6, 3, 14, 11, 14, 6…..   Round the final answer to one decimal place.
20. A poll was conducted during the final game of the basketball season to determine whether fans wanted to see the defending champions win the game or the challenging team win the game. From the poll, 216of the 374residents sampled from … urban areas want the defending champions to win the game. In more rural areas, 304 of the 466 residents polled want the defending champions to win the game. Assuming location has nothing to do with team preference, the probability that the data gathered was the result of chance is calculated to be 03. What is the correct interpretation of this calculation?
21. Find the mode of the following amounts (in thousands of dollars) in savings accounts of randomly selected people aged 25-30…… 8,6,8,7,2,2,2,4,4,4,4,7
22. A deck of cards contains red cards numbered 1,2,3,4,5, blue cards numbered 1,2,3,4,5,6,7,8and green … cards numbered 1,2,3,4,5,6,7,8,9,10. If a single card is picked at random, what is the probability that the card is green?…… Give your answer as a fraction.
23. The five-number summary for a set of data is … below…….What is the interquartile range of the set of data?
24. The five-number summary for a set of data is … below……..What is the interquartile range of the set of data?
25. The following frequency table summarizes a set … of data. What is the five-number summary?

# MATH 225N Week 5 Discussion, The Normal Distribution

Many variables in medicine follow a normal distribution where there are approximately an equal number of values below the … mean as above the mean. Describe two variables that you work with that would probably follow a normal distribution. Also note which of the two variables would be likely to have a larger standard deviation and why…

# MATH 225N Week 5 Lab Assignment

Scenario/Summary

This week’s lab highlights the use of probability and normal distribution.
Follow the directions below to gather data, calculate using Excel spreadsheets, and interpret the results.

Steps to Complete Week 5 Lab

Step 1: Survey or measure 10 people to find their heights. Determine the mean and standard deviation for this group by using the Week 3 Excel spreadsheet. Post a screen shot of the portion of the spreadsheet that helped you determine these values. How does your height compare to the mean (average) height of the group that you surveyed? Is your height taller, shorter, or the same as the mean of your group?
https://lms.courselearn.net/lms/content/1560/56100/MATH 225/w5lab1.jpgData Example of 10 people with different heights

Step 2: Give some background information on the group of people you used in your study. You might consider using the following questions to guide your answer.

• How did you choose the participants for your study (sampling method)?
• What part of the country did your study take place in?
• What are the age ranges of your participants?
• How many of each gender did you have in your study?

Step 3: Use the Week 5 Excel spreadsheet for the following.

• (Use the Empirical Rule tab from the spreadsheet). Determine the 68%, 95%, and 99.7% values of the Empirical Rule in terms of the ten heights in your height study.
• What do these values tell you?
• Post a screen shot of your work from the Week 5 Excel spreadsheet.
• (Use the normal probability tab from the spreadsheet). Based on your study results, what percent of the study participants are … shorter than you? What percent are taller than you?
• Post a screen shot of your work from the Week 5 Excel spreadsheet.

Step 4: Be sure your name is on the Word document, save it, and then submit it under “Assignments” and “Week 5: Lab”.

# MATH 225N Week 6 Discussion, Confidence Interval

Confidence Intervals

In everyday terms, a confidence interval is the range of values around a sample statistic (such as mean or proportion) within which clinicians can expect to get the … same results if they repeat the study protocol or intervention, including measuring the same outcomes the same ways. As you ask yourself, “Will I get the same results if I use this research?”, you must address the precision of study findings, which is … by the Confidence Interval. If the CI around the sample statistic is narrow, you can … confident you will get close to the same results if you implement the same research in your practice.

Consider the following example. Suppose that you did a systematic review of studies on the effect of tai chi exercise on sleep quality, and you found that … tai chi affected sleep quality in older people. If, according to your study, you found the lower boundary of the CI to … .49, the study statistic to … 0.87, and the upper boundary to … 1.25, this would mean that each end limit is 0.38 from the sample statistic, which is a relatively narrow CI.

(UB + LB)/2 = Statistic [(1.25 + .49)/2 = .87]

Keep in mind that a mean difference of 0 indicates there is no difference; this CI does not contain 0. Therefore, the sample statistic is statistically significant and unlikely to occur by chance.

Because this was a systematic review, and tai chi exercise has been established from the studies you assessed as helping people sleep, based on the sample statistics and the CI, clinicians could now use your study and confidently include tai chi exercises … among possible recommendations for patients who have difficulty sleeping.

Now you can apply your knowledge of CIs to create your own studies and make wise decisions about whether to base your patient care on a particular research finding.

Initial Post Instructions

Thinking of the many variables tracked by hospitals and doctors’ offices, confidence intervals could … created for population parameters (such as means or proportions) that were … calculated from many of them.

Choose a topic of study that is tracked (or you would like to see tracked) from your place of work. Discuss the variable and … parameter (mean or proportion) you chose, and explain why you would these to create an interval that captures the true value of the parameter of patients with 95% confidence.

Consider the following:

How would changing the confidence interval to 90% or 99% affect the study? Which of these values (90%, 95%, or 99%) would best suit … confidence level according to type of study chosen? How might the study findings … presented to those in charge in an attempt to affect change at the workplace?

# MATH 225N Week 6 Quiz Statistics – Question and Answers

1. A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she the mean score out of … 100points was a x¯=77, with a margin of error of 10……Construct a confidence interval for the mean score (out of 100 points) on the final exam.
2. A random sample of adults was… whether they prefer reading an e-book over a printed book. The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who … preferred reading an e-book……Use the empirical rule to construct a 95%confidence interval for the true proportion of adults who prefer e-books.
3. The pages per book in a library are normally … with an unknown population mean. A random sample of books is taken and … results in a 95%confidence interval of (237,293) pages……What is the correct interpretation of the 95% confidence interval?
4. The population standard deviation for the heights of dogs, in inches, in a city is 7inches. If we want to be 95% … that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can take? Round up to the nearest integer.
5. Clarence wants to estimate the percentage of students who live more than three miles from the school. He wants to create a 98%confidence interval which has an error bound of at most 4%. How many students should poll to create the confidence interval?
6. The average score of a … random sample of 87senior business majors at a university who took a certain standardized test follows a normal distribution with a standard deviation of 28. Use Excel to determine a 90% confidence interval for the mean of the population. Round your answers to two decimal places and use ascending order..
7. A random sample of 28statistics tutorials was from the past 5 years and the percentage of students absent from each … one recorded. The results are given below. Assume the percentages of students’ absences are approximately normally distributed. Use Excel to estimate the mean percentage of absences per tutorial over the past 5 years with 90% Round your answers to two decimal places and use increasing order.
8. Eric is studying people’s typing habits. He surveyed 525people and asked whether they leave one space or two spaces … after a period when typing. 440 people responded that they leave one space. Create a 90% confidence interval for the proportion of people who leave one space after a period…… Round your results to four decimal places.
9. A sample of 27employees for the Department of Health and Human Services has the following salaries, in thousands of dollars. Assuming normality, use Excel to find the 98% confidence interval for the true mean salary, in thousands of dollars. Round your answers to two decimal places and use increasing order.
10. The population standard deviation for the heights of dogs, in inches, in a city is 7inches. If we want to be 95%confident that … the sample mean is within 1 inch of the true population mean, what is the minimum sample size that can be taken?….z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576….Use the table above for the z-score, and be sure to round up to the nearest integer.
11. A random sample of house sizes in major city has a sample mean of x¯=1204.9sq ft and sample standard deviation of s=124.6sq ft.  Use the Empirical Rule to determine the approximate percentage of house sizes that lie between 7and 1454.1 sq ft…… Round your answer to the nearest … whole number (percent).
12. The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation.
13. The resistance of a strain gauge is normally distributed with a mean of 100ohms and a standard deviation of 3ohms. To meet the specification, the … resistance must be within the range 100±0.7 ohms. What proportion of gauges is acceptable? Round your answer to four decimal places.
14. A baker knows that the daily demand for strawberry pies is a random variable that follows the normal distribution with a … mean of 8pies and a standard deviation of 4.5pies. Find the demand that has an 8% probability of being exceeded………Use Excel, and round your answer to two decimal places.
15. A group of friends has gotten very competitive with their board game nights. They have found that overall, they each have won an average of 18games, with a population standard deviation of 6If a sample … of only 2 friends is … at random from the group, select the expected mean and the standard deviation of the sampling distribution from the options below. Remember to round to the nearest whole number.
16. An elementary school has a population of 635students, 600of whom have received the chicken pox vaccine. The school nurse wants to make sure that the school meets all state requirements for vaccinations at … public schools……Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=120…….. Round all answers to 3 decimal places.
17. The lengths of text messages are normally … with an unknown population mean. A random sample of text messages is taken and … results in a 95% confidence interval of (23,47)characters…What is the correct interpretation of the 95%  confidence interval?
18. Given the plot of normal distributions Aand Bbelow, which of the following statements is true? Select all correct answers. A normal bell curve labeled Upper A and a normal elongated curve labeled Upper B are at the same point. Normal curve Upper B is narrower and above normal curve Upper A.
19. A tour guide company is trying to decide if it is going to increase the cost of its tours to cover its sunk costs. They find that the average sunk cost per tour is \$58, with a standard deviation of \$18. If they take a random sample of 36tours, identify each of the following to help them make their decision and round to the nearest hundredth if necessary:
20. From a recent company survey, it is … that the proportion of employees older than 55and considering retirement is 8%. For a random sample of size 110, what is standard deviation for the sampling distribution of the … sample proportions, rounded to three decimal places?
21. In order to estimate the average electricity usage per month, a sample of 125residential customers were … , and the monthly electricity usage was … using the customers’ meter readings. Assume a population variance of 12,100kWh2. Use Excel to find the 98%confidence interval for the … mean electricity usage in kilowatt-hours. Round your answers to two decimal places and use ascending order.
22. Hugo averages 40words per minute on a typing test with a standard deviation of 15words per minute. Suppose Hugo’s words per minute on a typing test are normally … Let X= the number of words per minute on a typing test. Then, X∼N(40,15)……..Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is ________. This z-score tells you that x=56 is ________ standard deviations to the ________ (right/left) of the mean, ________……..Correctly fill in the blanks in the statement above.
23. Hugo averages 62words per minute on a typing test with a standard deviation of 8words per minute. Suppose Hugo’s words per minute on a typing test are normally … Let X= the number of words per minute on a … typing test. Then, X∼N(62,8)…….Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is ________. This z-score tells you that x=56 is ________ standard deviations to the ________ (right/left) of the mean, ________………Correctly fill in the blanks in the statement above.
24. Lisa has collected data to find that the number of pages per book on a bookshelf has a normal distribution. What is the probability that a random… book has fewer than 168pages if the mean is 190pages and the … standard deviation is 22 pages? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary.
25. Lisa has collected data to find that the number of pages per book on a bookshelf has a normal distribution. What is the probability that a random… book has fewer than 140pages if the mean is 190pages and the standard deviation is 25 pages? Use the empirical rule. Enter your answer as a percent rounded to … two decimal places if necessary.

# MATH 225N Week 6 Confidence Intervals Questions and Answers

1. On a busy Sunday morning, a waitress randomly sampled customers about their preference for morning beverages, Specifically, she wanted to … find out how many people preferred coffee over tea. The proportion of customers that … coffee was 0.42 with a margin of error 0.07. Construct a confidence interval for the proportion of customers that preferred coffee.
2. A company sells juice in 1quart bottles. In a quality control test, the company found the mean volume of juice in a random sample of … bottles was X = 31 ounces, with a marginal error of 3 ounces. ….. Construct a confidence interval for the mean number of ounces of juice bottled by this company.
3. Randomly … employees at an office … to take part in a survey about overtime. The office manager wanted to find out how many employees worked overtime in the last week.  The proportion of employees that … worked overtime was 0.83, with a margin of error of 0.11.
4. A random sample or garter snakes … , and the proportion of snakes that were longer than 20 inches in length recorded. The measurements resulted in a sample proportion of p = 0.25 with a sampling standard deviation of Op = 0.05. ……. Write a 68% confidence interval for the true proportion of garter snakes that were over 20 inches in length.
5. The average number of onions needed to make French onion soup from the population of recipes is unknown. A random sample of … recipes yields a sample mean of x = 8.2 onions.  Assume the sampling distribution of the mean has a standard deviation of 2.3 onions. ……. Use the Empirical Rule to construct a 95% confidence interval for the true population mean number of onions.
6. In a survey, a random sample of adults … whether a tomato is a fruit or vegetable. The survey resulted in a sample proportion of 0.58 with a sampling standard deviation of 0.08 … a tomato is a fruit. ……. Write a 99.7 confidence interval for the true proportion of number of adults … the tomato is a fruit.
7. A college admissions director wishes to estimate the mean number of students currently enrolled. The age of random sample of 23 students is … Assume the ages are approximately normally …  Use Excel to construct a 90% confidence interval for the population mean age.  Round your answer to 2 decimal places and use increasing order. ……. Use week 6 worksheet to get mean and SD.
8. Suppose that the scores of bowlers in a particular league follow a normal distribution such that a standard deviation of the population is 12. Find the 95% confidence interval of the mean score for all bowlers in this league using the … accompanying data set of 40 random scores. Round your answers to 2 decimal places using ascending order.
9. In the survey of 603 adults, 98 said that they regularly lie to people conducting surveys. Create a 99% confidence interval for the proportion of adults who regularly lie to people conducting surveys.  Use excel to create the confidence interval rounding to …4 decimal places.
10. In a random sampling of 350 attendees at a minor league baseball game, 184 said that they bought food from the concession stand. Create a 95%confidence interval for the proportion of fans who bought food from the concession stand.  Use excel to create the confidence interval rounding to 4 decimal places.
11. Suppose that the weight of tight ends in a football league are normally … such that sigma squared = 1,369. A sample of 49 tight ends was randomly … and the weights are …  Use Excel to create a 95% confidence interval for the … mean weight of the tight ends in this league.  Rounding your answers to 2 decimal places and using ascending order.   (Have to get square root of 1369 which is 37).  Population sample is yes .
12. Suppose heights, in inches of orangutans are normally … and have a known population standard deviation of 4 inches. A random sample of 16 orangutans is … a sample mean of 56 inches.  Find the confidence interval of the population mean with a 95% confidence level.
13. The population standard deviation for the total snowfalls per year in a city is 13 inches. If we want to … 95% confident that the sample mean is within 3 inches of the true population mean, what is the minimum sample size that should … taken?
14. The population standard deviation for the body weights for employees of a company is 10 pounds. If we want to … 95% confident that the … sample mean is within 3 pounds of the true population mean, what is the minimum sample size that should … taken.
15. The length, in words, of the essays written for a contest are normally distributed with a population standard deviation of 442 words and an unknown population mean.  If random sample of 24 essays is taken and results in a sample mean of 1330 words, find a 99% confidence interval for the population mean.  Round to two decimal places.
16. Brenda wants to estimate the percentage of people who eat fast food at least once per week. She wants to create a 95% Confidence interval which has an error bound of at most 2%.  How many people should … polled to create the confidence interval?
17. Suppose a clothing store wants to determine the current percentage of customers who are over the age of forty. How many customers should … the company survey in order to … 92% confident that the estimated (sample) proportion is within 5% of the true population proportion of customers who are over the age of 40?
18. Suppose the scores of a standardized test are normally …. If the population standard deviation is 2points, what minimum sample size is needed to … 90% confident that the sample mean is within 1 point of the true … population mean? … sure to round up to the nearest integer.
19. The number of square feet per house are normally … with a population standard deviation of 197square feet and an unknown population mean. If a random sample of 25 houses is taken and results in a sample mean of 1820 square feet, find a 99% confidence interval for the population mean. Round to 2 decimal places.
20. Suppose scores of a standardized test are normally … and have a known population standard deviation of 6points and an unknown population mean. A random sample of 22 scores is taken and gives a sample mean of 92 ……. Identify the parameters needed to calculate a confidence interval at the 98% confidence level. Then find the confidence interval.
21. Suppose scores of a standardized test are normally … and have a known population standard deviation of 6points and an unknown population mean. A random sample of 22 scores is taken and gives a …sample mean of 92 ……. What is the correct interpretation of the 95% confidence interval?
22. The weights of running shoes are normally distributed with a population standard deviation of 3ounces and an unknown population mean. If a random sample of 23 running shoes is taken and results in a … sample mean of 18 ounces, find a 90%confidence interval for the population mean.  Round the final answer to two decimal places.
23. The germination periods, in days, for grass seed are normally distributed with a population standard deviation of 5days and an unknown population mean. If a random sample of 17 types of grass seed is taken and results in a sample mean of 52days, find a 80% confidence interval for the population mean.
24. The speeds of vehicles traveling on a highway are normally distributed with a population standard deviation of 7miles per hour and an unknown population mean. If a random sample of 20 vehicles is taken and … results in a sample mean of 60miles per hour, find a 98% confidence interval for the population mean. Round the final answer to two decimal places.
25. Suppose finishing time for cyclists in a race are normally distributed and have a known population standard deviation of 6minutes and an unknown population mean. A random sample of 18cyclists is taken and gives a sample mean of 146 ……. Find the confidence interval for the population mean with a 99% confidence level.
26. Suppose the germination periods, in days, for grass seed are normally distributed. If the population standard deviation is 3days, what minimum sample size is needed to … 90%confident that the sample mean is … within 1 day of the true population mean?
27. Suppose the number of square feet per house is normally distributed. If the population standard deviation is 155square feet, what minimum sample size is needed to … 90% confident that the sample mean is within 47 square feet of the true population mean?
28. In a survey of 1,000adults in a country, 722 said that they had eaten fast food at least once in the past month. Create a 95% confidence interval for the population proportion of adults who ate fast food at least once in the past month. Use Excel to create the confidence interval, rounding to four decimal places.
29. A college admissions director wishes to estimate the mean age of all students currently enrolled. The age of a random sample of 23students is given below. Assume the ages are approximately normally distributed. Use Excel to construct a 90% confidence interval for the population mean age. Round your answers to two decimal places and use increasing order.
30. The yearly incomes, in thousands, for 24random married couples living in a city are given below. Assume the yearly incomes are … approximately normally distributed. Use Excel to find the 95% confidence interval for the true mean, in thousands. Round your answers to three decimal places and use increasing order.
31. tax assessor wants to assess the mean property tax bill for all homeowners in a certain state. From a survey ten years ago, a sample of 28property tax bills is given below. Assume the property tax bills are approximately normally distributed. Use Excel to construct a 95% confidence interval for the population mean property tax bill. Round your answers to two decimal places and use increasing order.
32. The table below provides a random sample of 20exam scores for a large geology class. Use Excel to construct a 90% confidence interval for the mean exam score of the class. Round your answers to one decimal place … and use ascending order.
33. Suppose scores on exams in statistics are normally distributed with an unknown population mean. A sample of 26scores is given below. Use Excel to find a 90% confidence interval for the true mean of statistics exam scores. Round your answers to one decimal place and use increasing order.
34. In a city, 22coffee shops are randomly … , and the temperature of the coffee sold at each shop is noted. Use Excel to find the 90% confidence interval for the population mean temperature. Assume the temperatures are approximately normally distributed. Round your answers to two decimal places and use increasing order.
35. Weights, in pounds, of ten-year-old girls are collected from a neighborhood. A sample of 26is given below. Assuming normality, use Excel to find the 98% confidence interval for the population mean weight μ. Round your answers to three decimal places and use increasing order.
36. A sample of 22test-tubes tested for … number of times they can … heated on a Bunsen burner before they crack is given below. Assume the counts are normally distributed. Use Excel to construct a 99% confidence interval for μ. Round your answers to two decimal places and use increasing order.
37. The monthly incomes from a random sample of 20workers in a factory is given below in dollars. Assume the population has a normal distribution and has standard deviation \$518. Compute a 98% confidence interval for the mean of the population. Round your answers to the nearest dollar and use ascending order.
38. Assume the distribution of commute times to a major city follows the normal probability distribution and the standard deviation is 5minutes. A random sample of 104 commute times is given below in minutes. Use Excel to find the 98%confidence interval for the mean travel time in minutes. Round your answers to one decimal place and use ascending order.
39. Installation of a certain hardware takes a random amount of time with a standard deviation of 7 A computer technician installs this hardware on 50different computers. These times are given in the accompanying dataset. Compute a 95% confidence interval for the mean installation time. Round your answers to two decimal places and use ascending order.
40. Assume that farm sizes in a particular region are normally distributed with a population standard deviation of 150 A random … sample of 50farm sizes in this region is … in acres. Estimate the mean farm size for this region with 90%confidence. Round your answers to two decimal places and use ascending order.
41. The amounts of time that customers stay in a certain restaurant for lunch is normally distributed with a standard deviation of 17 A random sample of 50lunch customers was taken at this restaurant. Construct a 99% confidence interval for the true average amount of time customers spend in the restaurant for lunch. Round your answers to two decimal places and use ascending order.
42. Recent studies have shown that out of 1,000children, 885 children like ice cream. What is the 99% confidence interval for the true proportion of children who like ice cream, based on this sample? Round z⋆ to two decimal places and other answers to four decimal places.
43. A large company is concerned about the … commute times of its employees. 333employees were surveyed, and 131employees said that they had a daily commute longer than 30 Create a 95% confidence interval for the proportion of employees who have a daily commute longer than 30 minutes. Use Excel to create the confidence interval, rounding to four decimal places.
44. The following data represent a random sample for the ages of 41players in a baseball league. Assume that the population is normally distributed with a standard deviation of 1 years. Use Excel to find the 98% confidence interval for the true mean age of players in this league. Round your answers to three decimal places and use ascending order.
45. In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 25pieces of carry-on luggage was collected and weighed in pounds. Assume that the population is normally distributed with … a standard deviation of 5 Find the 95% confidence interval of the mean weight in pounds. Round your answers to two decimal places and use ascending order.
46. A company wants to determine a confidence interval for the average CPU time of its teleprocessing transactions. A sample of 70random transactions in milliseconds is given below. Assume that the transaction times follow a normal distribution with a standard deviation of 600 Use Excel to determine a 98% confidence interval for the average CPU time in milliseconds. Round your answers to the nearest integer and use ascending order.
47. The number of hours worked per year per adult in a state is normally distributed with a standard deviation of 37. A sample of 115adults is … at random, and the number of hours worked per year per adult is given below. Use Excel to calculate the 98% confidence interval for the mean hours worked per year … for adults in this state. Round your answers to two decimal places and use ascending order.
48. An automobile shop manager timed 27employees and recorded the time, in minutes, it took them to change a water pump. Assuming normality, use Excel to find the 99% confidence interval for the true mean. Round your answers to three decimal places and use increasing order.
49. A type of golf ball is tested by dropping it onto a hard surface from a height of 1 The height it bounces is known to … normally: distributed. A sample of 25balls is tested and the bounce heights are given below. Use Excel to find a 95%confidence … interval for the mean bounce height of the golf ball. Round your answers to two decimal places and use increasing order.
50. The heart rates for a group of 21students taking a final exam are given below. Assume the heart rates are normally distributed. Use Excel to find the 95% confidence interval for the true mean. Round your answers to two decimal places and use increasing order.
51. Suppose a clothing store wants to determine the current percentage of customers who are over the age of forty. How many customers should the company survey in order to … 90% confident that the estimated (sample) proportion is within 4percentage points of the true population proportion of customers who are over the age of forty?
52. Virginia wants to estimate the percentage of students who live more than three miles from the school. She wants to create a 95%confidence interval which has an error bound of at most 5%. How many students should … polled to create the confidence interval?
53. Suppose an automotive repair company wants to determine the current percentage of customers who keep up with regular vehicle maintenance. How many customers should the company survey in order to … 95%confident that … the estimated (sample) proportion is within 4 percentage points of the true population proportion of customers who keep up with regular vehicle maintenance?
54. Suppose a clothing store wants to determine the current percentage of customers who are over the age of forty. How many customers should the company survey in order to … 92%confident that the estimated (sample) proportion is within 5percentage points of the true population proportion of customers who are over the age of forty?
55. The average height of a population is … unknown. A random sample from the population yields a sample mean of x¯=66.3 Assume the sampling distribution of the mean has a standard deviation of σx¯=0.8inches.
56. In a random sample of 30young bears, the average weight at the age of breeding is 312 Assuming the population ages are normally distributed with a population standard deviation is 30 pounds, use the Empirical Rule to construct a 68%confidence interval for the population average of young bears at the age of breeding. Do not round intermediate calculations. Round only the final answer to the nearest pound. Remember to enter the smaller value first, then the larger number.
57. In a food Questionnaire, a random sample of teenagers … whether they like pineapple pizza. The Questionnaire resulted in a sample proportion of p′=0.43, with a sampling standard deviation of σp′=0.06, who like this type of pizza. …… Write a 7%confidence interval using the Empirical Rule for the true proportion of teenagers who like pineapple pizza.
58. A marine biologist is interested in whether the Chinook salmon, a particular species of salmon in the Pacific Northwest, are getting smaller within the last decade. In a random sample of this species of salmon, she found the mean length was x¯=36inches with a margin of error of 9 ……. Construct a confidence interval for the mean length of Chinook salmon.
59. A researcher is trying to estimate the population mean for a certain set of data. The sample mean is 45, and the … error bound for the mean is 9, at a 7%confidence level. (So, x¯=45 and EBM = 9.) Find and interpret the confidence interval estimate.
60. A random sample of registered voters … about an issue on the ballot of an … election. The proportion of those surveyed who plan to vote “Yes” on the issue is 54, with a margin of error of 0.06 …….. Construct a confidence interval for the proportion of registered voters that plan to vote “Yes” on the issue.

# MATH 225N Week 7 Hypothesis Testing Question and Answers

1. Steve listens to his favorite streaming music service when he works out. He wonders whether the service algorithm does a good job … of finding random songs that he will like more often than not.  To test this, he listens to 50 songs chosen by the service at random and finds that he likes 32 of them.
2. A magazine regularly tested products and gave the reviews to its customers. In one of its reviews, it tested 2 types of batteries and … claimed that the batteries from company A outperformed batteries from company B in 108 of the tests.  There were 200 tests.  Company B decided to sue the magazine, claiming that the results were not significantly different from 50% and that the magazine was slandering its good name.
3. A candidate in an election lost by 5.8% of the vote. The candidate sued the state and said that more than 5.8% of the ballots were … defective and not counted by the voting machine, so a full recount would need to be done.  His opponent wanted to ask for the case to be dismissed, so she had a government official from the state randomly select 500 ballots and count how many were defective. The official found 21 defective ballots.
4. A researcher claims that the incidence of a certain type of cancer is < 5%. To test this claim, a random sample of 4000 people are … and 170 are found to have the cancer.
5. A researcher is investigating a government claim that the unemployment rate is < 5%. TO test this claim, a random sample of 1500 people is … and it is determined that 61 people were unemployed.
6. An economist claims that the proportion of people that plan to purchase a fully electric vehicle as their next car is greater than 65%.
7. Colton makes the claim to his classmates that < 50% of newborn babies born this year in his state are boys. To prove this claim, he selects a … random sample of 344 birth records in his state from this year.  Colton found that 176 of the newborns were boys.  What are the null and alternative hypothesis for this hypothesis test.
8. An Airline company claims that in its recent advertisement that at least 94% of passenger luggage that is lost is recovered and reunited with their customer within 1 day. Hunter is a graduate student studying statistics. For a research project, Hunter wants to find out whether there is sufficient evidence in support of the … airline company’s claim.  He randomly selects 315 passengers whose luggage was lost by the airlines and found out that 276 of those passengers were reunited with their luggage within 1 day. Are all of the conditions for his hypotheses test met, and if so, what are the Ho and Ha for this hypothesis test?
9. A college administrator claims that the proportion of students who are nursing majors is > 40%. To test this claim, a group of 400 students are randomly … selected and its determined that 190 are nursing majors.  The following is the set up for the hypothesis test:  Ho: p = .40 and Ha: p = >.40
10. A hospital administrator claims that the proportion of knee surgeries that are successful are 87%. To test this claim, a random … sample of 450 patients who underwent knee surgery is taken and it is determined that 371 patients had a successful knee surgery operation. Ho:  p = 0.87 Ha: p  (two sided tail)
11. Jose, a competitor in cup stacking, has a sample stacking time mean of 7.5 seconds from 13 trials. Jose still claims that his average stacking time is 8.5 seconds, and the low average can be contributed to chance.  At the 2% significant level, does the data provide sufficient evidence to conclude that Jose’s mean stacking time is less than 8.5 seconds? Given the sample data below, select or reject the hypothesis.  (If p=value is < alpha value, we would automatically reject the hypothesis)
12. Marty, a typist, claims his average typing speed is 72 wpm. During a practice session, Marty has a sample typing speed mean of 84 wpm based on 12 trials. At the 5% significance level, does the data provide sufficient evidence to … conclude that his mean typing speed is >72 wpm? Accept or reject the hypothesis given the data below.
13. What is the p-value of a two-tailed one mean hypothesis test, with a test statistic of Zo = 0.27? (Do not round your answer.  Compute your answer using a value from the table. (Value in table was 0.606)
14. Raymond, a typist, claims his average typing speed is 89 wmp. During a practice session, Raymond has a sample typing speed mean of 95.5 wmp based on 15 trials. At the 1% significance level, does the data provide sufficient evidence to conclude that his mean typing speed is > 89 wmp? Accept or reject the hypothesis given the sample data below:
15. Kurtis is a statistician who claims that the average salary of an employee in the city of Yarmouth is no more than \$55,000 per year. Gina, his colleague, believes this to be incorrect, so she randomly selects 61 employees who work in Yarmouth and … record their annual salary.  Gina calculates the sample mean income to be \$56.500 per year with a sample standard deviation of \$3750.  Using the alternative hypothesis, Ha = , find the test statistic  and the p-value for the appropriate hypothesis test. Round the  to 2 decimal places and the p-value to 3 decimal places.
16. A college administrator claims that the proportion of students that are nursing majors is less than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 149 are nursing majors.
17. A researcher claims that the incidence of a certain type of cancer is less than 5%. To test this claim, the a random sample of 4000people are … checked and 170 are determined to have the cancer.
18. A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of 200drivers is taken and its determined that 126 people are wearing seat belts.
19. A police officer claims that the proportion of accidents that occur in the daytime (versus nighttime) at a certain intersection is 35%. To test this claim, a random sample of 500 accidents at this intersection was examined … from police records it is determined that 156 accidents occurred in the daytime.
20. A teacher claims that the proportion of students expected to pass an exam is greater than 80%. To test this claim, the teacher administers the test to 200random students and  determines that 151 students pass the exam.
21. A researcher claims that the proportion of smokers in a certain city is less than 20%. To test this claim, a random sample of 700people is taken in the city and 150 people indicate they are smokers.
22. A researcher claims that the proportion of people who are right-handed is 70%. To test this claim, a random sample of 600 people is taken and its determined that 397 people are right handed.
23. Kathryn, a golfer, has a sample driving distance mean of 3yards from 13 drives. Kathryn still claims that her average driving distance is 207 yards, and the low average can … to chance. At the 1% significance level, does the … data provide sufficient evidence to conclude that Kathryn’s mean driving distance is less than 207 yards? Given the sample data below, accept or reject the hypothesis.
24. Mary, a javelin thrower, claims that her average throw is 61 During a practice session, Mary has a sample throw mean of 55.5meters based … on 12 throws. At the 1% significance level, does the data provide sufficient evidence to conclude that Mary’s mean throw is less than 61 meters? Accept or reject the hypothesis given the sample data below.
25. Elizabeth claims that her average typing speed is … at least 87words per minute……. From recent typing trials, it is observed that Elizabeth has a sample typing speed mean of 98.9 words per minute (based on 18 trials)……Given the sample data below, determine whether to reject the null hypothesis, or fail to reject the null hypothesis and also come to a conclusion regarding the claim.
26. Shawn, a competitor in cup stacking, has a sample stacking time mean of 2seconds from 13 trials. Shawn still claims that her average stacking … time is 8.5 seconds, and the high average can be attributed to chance. At the 4% significance level, does the data provide sufficient evidence to conclude that Shawn’s mean stacking time is greater than 8.5 seconds? Given the sample data below, accept or reject the hypothesis.
27. Ruby, a bowler, has a sample game score mean of 8from 25 games. Ruby still claims that her average game score is 140, and the low average can … attributed to chance. At the 5% significance level, does the data … provide sufficient evidence to conclude that Ruby’s mean game score is less than 140? Given the sample data below, accept or reject the hypothesis.
28. Timothy, a bowler, has a sample game score mean of 1from 11 games. Timothy still claims that his average game score is 182, and the high average can … attributed to chance. At the 5% significance level, does the data provide sufficient evidence to conclude that Timothy’s mean game score is greater than 182? Given the … sample data below, accept or reject the hypothesis.
29. What is the p-value of a two-tailed one-mean hypothesis test, with a test statistic of z0=−1.59? (Do not round your answer; compute your answer using a value from the table below.)
30. What is the p-value of a left-tailed one-mean hypothesis test, with a test statistic of z0=−1.19?
31. What is the p-value of a left-tailed one-mean hypothesis test, with a test statistic of z0=−65? (Do not round your answer; compute your answer using a value from the table below.
32. What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=36? (Do not round your answer; compute your answer using a value from the table below.)
33. What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=82? (Do not round your answer; compute your … answer using a value from the table below.) Number in table was 0.966. So 1-.966 = 0.034
34. What is the p-value of a two-tailed one-mean hypothesis test, with a test statistic of z0=−73? (Do not round your answer; compute your … answer using a value from the table below.) Table # was 0.042 so 0.042 * 2 = 0.084
35. A CEO wondered if her company received either more or less complaints from its workers on Monday than any other day. She figured that if it were truly random, 20%of the complaints should have been … on Monday. She randomly selected 50 complaints and checked the day that they were …. In those complaints 13 were submitted on a Monday.
36. The CEO conducts a one-proportion hypothesis test at the 5%significance level, to test whether the true proportion of complaints … on a Monday is different from 20%…….  Which answer choice shows the correct null and alternative hypotheses for this test?
37. A CEO wondered if her company received either more or less complaints from its workers on Monday than any other day. She figured that if it were truly random, 20%of the complaints … on Monday. She randomly … 50complaints and … the day that they were …. In those complaints 13 were …. The CEO conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of complaints … on a Monday is different from 20%.
38. A business owner claims that the proportion of take out orders is greater than 25%. To test this claim, the owner checks the next 250orders and determines that 60 orders are take out orders…… The following is the setup for … this hypothesis test:….. {H0:p=0.25Ha:p>0.25 …….Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
39. Colton makes the claim to his classmates that less than 50%of newborn babies born this year in his state are boys. To prove this … claim, he selects a random sample of 344 birth records in his state from this year. Colton found that 176 of the newborns are boys. What are the null and alternative hypotheses for this hypothesis test?
40. Kylie works for a large nursery and is investigating whether to use a new brand of seeds. The new brand of seeds advertises that 93%of the seeds germinate, which is higher than the germination rate of the seeds she is … currently using. She will change over to this new brand unless the actual germination rate is less than what is … Kylie conducts an experiment by randomly selecting 76 seeds of the new brand and plants them. She finds that 70 of those seeds germinated. What are the null and alternative hypotheses for this hypothesis test?
41. The owners of a supermarket chain are looking into the effectiveness of the supermarket’s loyalty card … program. Specifically, they would like to know if the percentage of shoppers in their stores who use the loyalty card has changed from 63%in 2014. Chloe works in the marketing department of the chain and is … to answer the owners’ inquiry. She randomly selects 196 customers from various stores in the chain and finds that 114 use the loyalty card. What are the null and alternative hypotheses for this hypothesis test?
42. A researcher claims that the proportion of college students who plan to participate in community service after graduation is greater than 35%.  To test this claim, a survey asked 500randomly selected college students if they planned to perform community service after graduation. Of those students, 195 indicated they planned to perform community service.
43. A researcher claims that the … proportion of people over 65 years of age in a certain city is greater than 11%. To test this claim, a sample of 1000people are … and its determine that 126 people are over 65 years of age…… The following is the setup for this hypothesis test:…… {H0:p=0.11Ha:p>0.11 ……. Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
44. Rosetta, a pitcher, claims that her pitch speed is more than 57miles per hour, on average. Several of her teammates … do not believe her, so she decides to do a hypothesis test, at a 1% significance level, to persuade them. She throws 10 The mean speed of the sample pitches is 64 miles per hour. Rosetta knows from experience that the standard deviation for her pitch speed is 4 miles per hour……. H0: μ≤57; Ha: μ>57….. α=0.01 (significance level)…… What is the test statistic (z-score) of this one-mean hypothesis test, … to two decimal places?
45. Which of the following results in a null hypothesis p≤0.61and alternative hypothesis p>0.61?
46. Suppose the null hypothesis, H0, is: a weightlifting bar can withstand weights of 800pounds and less. What is α, the probability of a Type I error in this scenario?
47. Suppose a pitcher claims that his … pitch speed is less than 43miles per hour, on average. Several of his teammates do not believe him, so the pitcher decides to do a hypothesis test, at a 10% significance level, to persuade them. He throws 19 The mean speed of the sample pitches is 35 miles per hour. The pitcher knows from experience that the standard deviation for his pitch speed is 6 miles per hour…… H0: μ≥43; Ha: μ<43……α=0.1 (significance level)……. What is the test statistic (z-score) of this one-mean hypothesis test, … to two decimal places?
48. Which graph below corresponds to the following hypothesis test?
49. Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70%of its customers do not shop at any other sporting goods stores. What is the Type I error in this scenario?
50. Which of the following results in a null hypothesis p≥44and alternative hypothesis p<0.44?
51. Determine the Type I error if the null hypothesis, H0, is: an electrician claims that no more than 10%of homes in the city are not up to the current electric codes.
52. Suppose the null hypothesis, H0, is: the mean age of the horses on a ranch is 6 What is the Type I error in this scenario?
53. What is β, the probability of a Type II error if the null hypothesis, H0, is: an electrician claims that no more than 10%of homes in the city are … not up to the current electric codes.
54. A consumer protection company is testing a towel rack to see how much force it can hold. The null hypothesis, H0, is that the … rack can hold at least 100pounds of force. The alternative hypothesis, Ha, is that the rack can hold less than 100pounds of force.
55. Suppose the null hypothesis, H0, is: the mean age of the horses on a ranch is 6 What is the Type II error in this scenario?
56. Determine the Type I error if the null hypothesis, H0, is: a wooden ladder can withstand weights of 250pounds and less.
57. Which of the following answers give valid null and alternative hypotheses for a hypothesis test?
58. A mattress store advertises that their beds last at least 5years, on average. A consumer group thinks that they do not last that long and … wants to set up a hypothesis test.
59. A mechanic wants to show that more than 44%of car owners do not follow a normal maintenance schedule. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p.
60. Which of the following results in a null hypothesis p≤0.69and alternative hypothesis p>0.69?
61. A city wants to show that the mean number of public transportation users per day is more than 5,575. Identify the … null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.
62. In 2015, the CDC analyzed whether American adults were eating enough fruits and vegetables. Let the mean cups of vegetables adults … eat in a day be μ. If the analysts wanted to know if adults were eating, on average, at least the … 2 cups of vegetables a day, what are the null and alternative hypothesis?
63. Which of the following results in a null hypothesis p≤0.47and alternative hypothesis p>0.47?
64. A hospital claims that the … mean wait time for emergency room patients is at least 55 A group of researchers believe that this is not accurate, and want to show that the mean wait time is less than 55minutes. Identify the group’s null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.
65. Which graph below corresponds to the following hypothesis test?
66. Which type of test is …. scenario: …… A manufacturer claims that the mean lifetime of a new cutting blade is 2 years. Fourteen blades are randomly … and their lifetime is …. Assume the population follows a normal distributions with known standard deviation.
67. Which graph below corresponds to the following hypothesis test?
68. Suppose the null hypothesis, H0, is: doctors believe that a surgical procedure is successful at least 80%of the time. Which of the … following gives β, the probability of a Type II error?
69. Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70%of its customers do not shop at any other sporting goods stores. What is β, the probability of a Type II error in this scenario?
70. Determine the Type II error if the null hypothesis, H0, is: the mean price of a loaf of bread is \$1.67.
71. Which of the following results in a null hypothesis μ≥31and alternative hypothesis μ<31?
72. Which of the following results in a null hypothesis μ≤7and alternative hypothesis μ>7?
73. A commonly cited study says that 49%of students study less than 5 hours per week. A researcher does not think this is accurate and wants to show that the percentage of students that study less than 5 hours per week is not equal to 49%……. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p.
74. Horace, a golfer, claims that his drive distance is less than 225meters, on average. Several of his friends do not believe him, so he decides to do a hypothesis test, at a 10% significance level, to persuade them. He hits 23 The mean … distance of the sample drives is 210 meters. Horace knows from experience that the standard deviation for his drive distance is 14meters……. H0: μ≥225; Ha: μ<225……. α=0.1 (significance level)…..What is the test statistic (z-score) of this one-mean hypothesis test, … to two decimal places?
75. William, a chef, claims that his meatball weight is not equal to 3ounces, on average. Several of his customers do not believe him, so he decides to do a hypothesis test, at a 1% significance level, to … persuade them. He cooks 19 The mean weight of the sample meatballs is 2.9 ounces. William knows from experience that the standard deviation for his meatball weight is 0.5 ounces……. H0: μ=3; Ha: μ≠3…… α=0.01 (significance level)……. What is the test statistic (z-score) of this one-mean hypothesis test, … to two decimal places?

# MATH 225N Week 7 Lab Assignment, Confidence Interval

The highlight of this week’s lab is confidence intervals and the use of these intervals in the health sciences. There is a short reading that … specifically relates confidence intervals to health sciences and then you are asked to demonstrate your knowledge of confidence intervals by applying them in a practical manner.

Steps to Complete the Week 7 Lab

Step 1: Find these articles in the Chamberlain Library. Once you click each link, you will be logged into the Library and then click on “PDF Full Text”.

• First Article: Confidence Intervals, Part 1 (Links to an external site.)
• Second Article: Confidence Intervals, Part 2 (Links to an external site.)

Step 2: Consider the use of confidence intervals in health sciences with these articles as inspiration and insights.

Step 3: Using the data you collected for the Week 5 Lab (heights of 10 different people that you work with), discuss your method of collection for the values that you are using in your study. What are some faults with this type of data collection? What other type of data collection could you have used, and how might this have … affected your study?

1. Give a point estimate for the average height of all people at the place where you work. Start by putting the ten heights you are working with into the blue Datacolumn of the spreadsheet. What is your point estimate, and what does this mean?
2. Find a 95% confidence interval for the true mean height of all the people at your place of work. What is the interval? … example of finding 95 percent confidence interval in spreadsheet
3. Give a practical interpretation of the interval you found in part b, and explain carefully what the output means. (For example, you might say, “I am 95% confident that the true mean height of all of the people in my company is between 64 inches and 68 inches”).
4. Post a screenshot of your work from the t value Confidence Interval for Âμfrom the Confidence Intervaltab on the Week 6 Excel spreadsheet

Step 5:

Now, find a 99% confidence interval for the …same data. Would the margin of error be larger or smaller for the 99% CI? Explain your reasoning.

Step 6:

Save the Week 7 Lab document with your answers and … include your name in the title.

Step 7:

Submit the document.

# MATH 225N Week 8 Questions with Answers

If a regression analysis was to … completed on body mass index (BMI), what could be an independent variable in that analysis? Why? If we could, what other … independent variables should … included in the analysis? What statistic(s) would show the value of that regression in understanding BMI? Alternatively, find an article that … uses regression analysis to study a medical concern. In that study, what was the dependent variable and what were the independent variable(s)? Further, how would you use … this study to highlight the difference between correlations and causation?

# MATH 225N Week 8 Discussion, Correlation and Regression

Performing Linear Regressions with Technology

1. An amateur astronomer is researching statistical properties of known stars using a variety of databases. They collect the absolute magnitude or MV and stellar mass or M⊙ for 30 stars. The … absolute magnitude of a star is the intensity of light that would be observed from the star at a distance of 10 parsecs from the star. This is measured in terms of a particular band of the light spectrum, indicated by the subscript letter, which in this case is V for the visual light spectrum. The scale is logarithmic and an MV that is 1 less than another comes from a star that is 10 times more luminous than the other. The stellar … mass of a star is how many times the sun’s mass it has. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets, rounding to two decimal places.
2. The table shows data collected on the relationship between the time spent studying per day and the time spent reading per day. The line of best fit for the data is yˆ=0.16x+36.2. Assume the line of best fit is significant and there is a strong linear relationship between the variables……. Studying (Minutes) 507090110 Reading (Minutes) 44485054…… (a) According to the line of best fit, what would be the predicted number of minutes spent reading for someone who spent 67 minutes studying? Round your answer to two decimal places.
3. The table shows data collected on the … relationship between the time spent studying per day and the time spent reading per day. The line of best fit for the data is yˆ=0.16x+36.2…… Studying (Minutes) 507090110 Reading (Minutes) 44485054…… (a) According to the line of best fit, the predicted number of minutes spent reading for someone who spent 67minutes studying is 46.92…… (b) Is it reasonable to use this line of best fit to make the above prediction?
4. Data is collected on the relationship between the average daily temperature and time spent watching television. The data is … shown in the table and the line of best fit for the data is y^=−0.81x+96.7. Assume the line of best fit is significant and there is a strong linear relationship between the variables……. Temperature (Degrees) 30405060 Minutes Watching Television 73635748……. (a) According to the line of best fit, what would be the predicted number of minutes spent watching television for an average daily temperature of 45 degrees? Round your answer to two … decimal places.
5. Data is collected on the relationship between the average daily temperature and time spent watching television. The data is … shown in the table and the line of best fit for the data is y^=−0.81x+96.7…… Temperature (Degrees) 30405060 Minutes Watching Television 73635748……. (a) According to the line of best fit, the predicted number of minutes spent watching television for an average daily temperature of 45 degrees is 25…….  (b) Is it reasonable to use this line of best fit to make the above prediction?
6. Homer is studying the relationship between the average daily temperature and time spent watching television and … has collected the data shown in the table. The line of best fit for the data is yˆ=−0.6x+94.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables……. Temperature (Degrees) 40506070 Minutes Watching Television 70655952….. According to the line of best fit, what would be the predicted number of minutes spent watching television for an … average daily temperature of 39 degrees? Round your answer to two decimal places, as needed.
7. Homer is studying the relationship between the average daily temperature and time spent watching television and has collected the data shown in the table. The line of best fit for the data is yˆ=−0.6x+94.5……. Temperature (Degrees) 40506070 Minutes Watching Television 70655952……. (a) According to the line of best fit, the … predicted number of minutes spent watching television for an average daily temperature of  39 degrees is 1. …….  (b) Is it reasonable to use this line of best fit to make the above prediction?
8. Daniel owns a business consulting service. For each consultation, he charges \$95plus \$70 per hour of work. A linear equation that expresses the total amount of money Daniel earns per consultation is y=70x+95. What are the independent and dependent variables? What is the y-intercept and the slope?
9. Given the following line, find the value of y when x=2. ……. y=−4x−12
10. Evaluate … the linear equation, y=4x−7, at the value x=2.
11. Evan owns a house cleaning service. For each house visit, he charges \$55plus \$30 per hour of work. A linear equation that expresses the total amount of money Evan earns per visit is y=55+30x…….. What are the independent and dependent variables? What is the y-intercept and the slope?
12. Using a calculator or statistical software, find the linear regression line for the data in the table below.……. Enter your answer in the form y=mx+b, with mand bboth rounded to two decimal places.
13. Using a calculator or statistical software, find the linear regression line for the data in the table below.……. Enter your answer in the form y=mx+b, with mand bboth rounded to two decimal places.
14. A least squares regression line (best-fit line) has the equation, yˆ=2.87x−43.5. What is the slope of this linear regression equation?
15. Researchers want to find the relationship between age and average weight in female children. Using a calculator or … statistical software, find the linear regression line for the 2012 CDC data below for average weights of female children by age.
16. Given that n=31data points are collected when studying the relationship between average daily temperature and time spent sleeping, use the critical values table below to determine if a … calculated value of r=−0.324is significant or not.
17. In studying the relationship between age and eating fast food, suppose you computed r=0.133using n=19data points. Using the critical values table below, determine if the value of r is significant or not.
18. Data is collected on the relationship between the time spent doing homework per day and the time … spent taking notes per day. The data is shown in the table and the line of best fit for the data is yˆ=0.175x+31.0. Assume the line of best fit is significant and there is a strong linear relationship between the variables…….. (a) According to the line of best fit, what would be the predicted number of minutes spent taking notes for someone who spent 137minutes doing homework? Round your answer to…  two decimal places, as needed.
19. Michelle is studying the relationship between the hours worked (per week) and time spent reading (per day) and has collected the data shown in the table. The line of best fit for the data is yˆ=−0.79x+98.8. Assume the line of best fit is significant and there is a strong linear relationship between the variables….. Hours Worked (per week) 30405060 Minutes Reading (per day) 75685852……. (a) According to the line of best fit, what … would be the predicted number of minutes spent reading for a person who works 27hours (per week)? Round your answer to two decimal places, as needed.
20. Michelle is studying the relationship between the hours worked (per week) and time spent reading (per day) and has collected the data shown in the table. The line of best fit for the data is yˆ=−0.79x+98.8……. Hours Worked (per week) 30405060 Minutes Reading (per day) 75685852……. (a) According to the line of best fit, the predicted number of minutes spent reading for a person who works 27hours (per week) is 77.47……..  (b) Is it reasonable to use this line of best fit to make the above prediction?
21. The table shows data collected on the relationship between time spent playing video games and time spent with family. The line of best fit for the data is yˆ=−0.24x+71.7. Assume the line of best fit is significant and there is a strong linear relationship between the variables…… Video Games (Minutes) 45607590 Time with Family (Minutes) 61575450……. (a) According to the line of best fit, what … would be the predicted number of minutes spent with family for someone who spent 87minutes playing video games? Round your answer to two decimal places.
22. The table shows data collected on the relationship between time spent playing video games and time spent with family. The line of best fit for the data is yˆ=−0.24x+71.7……. Video Games (Minutes) 45607590 Time with Family (Minutes) 61575450…… (a) According to the line of best fit, the predicted number of minutes spent with family for someone who spent 87 minutes playing video games is 50.82……..  (b) Is it reasonable to use this line of best fit to make … the above prediction?
23. A scientific study on calorie intake gives the following data table…….. Using technology, it was determined that the total sum of squares (SST)was 76, the sum of squares regression (SSR)was 54.850, and the sum of squares due to error (SSE)was 21.150. Calculate R2 and determine its meaning. Round your answer to four decimal places?
24. A non-profit finds that donations decrease when the economy measured by GDP decreases……..  Identify the relation between donations and GDP.
25. Which of the following data sets or plots … could have a regression line with a negative slope.
26. A gym teacher finds that the distance students run in miles per week in gym class, D, is dependent on the time students warm-up beforehand in minutes per week, x, and can be modeled by the function……. D(x)=2+0.5x…….. Draw the graph of the distance function … by plotting its D-intercept and another point.
27. Which of the following data sets or plots could have a regression line with a negative y-intercept