Description
Week 6: Confidence Interval
Week | Assignments | Due Date |
Week 6 | Graded Discussion | Suggested Due Date—
Initial Post: Wednesday of Week 6
Due Date— Responses: Sunday of Week 6 [Have two posts on two different days] |
Knewton Homework Assignments
Confidence Interval for Mean – Population Standard Deviation Known Confidence Intervals – Empirical Rule Estimating Sample Size for a Population Proportion Point Estimates, Margins of Error, and Confidence Intervals Understanding Confidence Intervals – Excel |
Sunday of Week 6 | |
Week 6 Quiz |
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Week 6 Assignment – Confidence Interval for Mean – Population Standard Deviation Known (2)
Activity 1
Question
Suppose the scores of a standardized test are normally distributed. If the population standard deviation is 4 points, what minimum sample size is needed to be 95% confident that the sample mean is within 1 point of the true population mean?
Use the table above for the z-score, and be sure to round up to the nearest integer.
Answer
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Activity 2
Question
Suppose the weights, in pounds, of the dogs in a city are normally distributed. If the population standard deviation is 3 pounds, what minimum sample size is needed to be 95% confident that the sample mean is within 1 pound of the true population mean?
Use the table above for the z-score, and be sure to round up to the nearest integer.
Answer
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Activity 3
Question
Suppose the finishing times for cyclists in a race are normally distributed. If the population standard deviation is 16 minutes, what minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean?
Use the table above for the z-score, and be sure to round up to the nearest integer.
Provide your answer below:
Answer
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Activity 4
Question
Suppose the germination periods, in days, for grass seed are normally distributed. If the population standard deviation is 3 days, what minimum sample size is needed to be 90% confident that the sample mean is within 1 day of the true population mean?
Use the table above for the z-score, and be sure to round up to the nearest integer.
Answer
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Activity 5
Question
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 a 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.
You may use a calculator or the common z values above.
Answer
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Activity 6
Question
Suppose the scores of a standardized test are normally distributed. If the population standard deviation is 2 points, what minimum sample size is needed to be 90% confident that the sample mean is within 1 point of the true population mean?
Use the table above for the z-score, and be sure to round up to the nearest integer.
Answer
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Activity 7
Question
The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 8 inches and an unknown population mean. A random sample of 25 snakes is taken and results in a sample mean of 58 inches.
Identify the parameters needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval.
You may use a calculator or the common z values above.
Answer
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Activity 8
Question
The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 8 inches and an unknown population mean. A random sample of 25 snakes is taken and results in a sample mean of 58 inches.
What is the correct interpretation of the confidence interval?
Select the correct answer below:
- We can estimate with 99% confidence that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.
- We can estimate with 99% confidence that the sample mean length of adult corn snakes is between 53.88 and 62.12 inches.
- We can estimate that 99% of adult corn snakes will have a length that is between 53.88 and 62.12 inches
Answer
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Activity 9
Question
The weights, in pounds, of dogs in a city are normally distributed with a population standard deviation of 2 pounds and an unknown population mean. A random sample of 16 dogs is taken and results in a sample mean of 28 pounds.
Identify the parameters needed to calculate a confidence interval at the 90% confidence level. Then find the confidence interval.
You may use a calculator or the common z values above.
Answer
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Activity 10
Question
The weights, in pounds, of dogs in a city are normally distributed with a population standard deviation of 2 pounds and an unknown population mean. A random sample of 16 dogs is taken and results in a sample mean of 28 pounds.
What is the correct interpretation of the confidence interval?
Select the correct answer below:
- We can estimate that 90% of the dogs in the city have a weight that lies between 27.18 and 28.82 pounds.
- We can estimate with 90% confidence that the sample mean weight of dogs in the city is between 27.18 and 28.82 pounds.
- We can estimate with 90% confidence that the true population mean weight of dogs in the city is between 27.18 and 28.82 pounds.
Answer
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Activity 11
Question
Suppose the heights of seasonal pine saplings are normally distributed. If the population standard deviation is 14 millimeters, what minimum sample size is needed to be 95% confident that the sample mean is within 4 millimeters of the true population mean?
Use the table above for the z-score, and be sure to round up to the nearest integer.
Answer
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Activity 12
Question
The population standard deviation for the scores of a standardized test is 4 points. If we want to be 90% confident that the sample mean is within 1 point of the true population mean, what is the minimum sample size that should be taken?
Use the table above for the z-score, and be sure to round up to the nearest integer.
Answer
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