[Top Answer] MATH225N – Week 1 Assignment – Comparing Sampling Methods

Description

Week 1 Assignment: Comparing Sampling Methods

Objectives

1.4 Comparing Sampling Methods

• Identify and distinguish between stratified, cluster, systematic, and convenience sampling
• Determine appropriate sampling methods

Activity 1

Question

Identify and Distinguish Between Stratified, Cluster, Systematic, and Convenience Sampling

Types of Sampling

A sample should have the same characteristics as the population it is representing. Most statisticians use various methods of random sampling in an attempt to achieve this goal. There are several different methods of random sampling. In each form of random sampling, each member of a population initially has an equal chance of being selected for the sample.

A simple random sample is a sample selected from a population in a way such that all combinations of members of the population of that size have the same chance of being selected. However, a true simple random sample can sometimes be difficult to obtain. Additionally, researchers may sometimes wish to ensure that some distinguishable characteristic of members in the population is not overrepresented or underrepresented in their sample, as could occur by chance with a simple random sample. Beyond simple random sampling, well-known random sampling methods include stratified sampling, cluster sampling, and systematic sampling.

To choose a stratified sample, you should divide the population into groups, and then take your sample from a proportionate number from each group.

Example

To choose a stratified sample of all students at your college, you could group all the students by the schools they belong to – Liberal Arts, Engineering, Journalism, or Business. To choose a simple random sample from each school, you could number each student in the Liberal Arts school, number each student in the Engineering school, and do the same for the remaining schools.

Then you would randomly choose a proportionate number of students from the Liberal Arts school, the Engineering school, the Journalism school, and the Business school. The combination of all students randomly chosen from each of these schools is the stratified sample.

To choose a cluster sample, divide the population into groups, and then randomly select some of the groups. All the members from these chosen groups are in the cluster sample.

Example

To choose a cluster sample of all students at your college, you could cluster all the students into their majors. You could number these majors (clusters), and then randomly choose five majors using simple random sampling. All students from these five majors make up the cluster sample.

To choose a systematic sample, randomly select a starting point and take every nth piece of data from a listing of the population. Systematic sampling is frequently chosen because it is a simple method.

Example

Suppose you have to do a phone survey, and you want a systematic sample. Your phone book contains 20,000 residence listings. You must choose 400 names for the sample. Number the population 1–20,000 and then use a simple random sample to pick a number that represents the first name in the sample. Then choose every 15th name thereafter until you have a total of 400 names. (You might have to go back to the beginning of your phone list.) Every person in that list of 400 names is in the systematic sample.

Activity 2

Question

True or False? Stratified sampling was used in the scenario below.

A random number generator is used to select a student from the alphabetical listing of all undergraduate students in the Fall semester. Starting with that student, every 50th student is chosen until 75 students are included in the sample.

Activity 3

Question

Identify and Distinguish Between Stratified, Cluster, Systematic, and Convenience Sampling

Convenience Sampling

A type of sampling that is not random is convenience sampling. (Stratified, cluster and systematic sampling are all random.) Convenience sampling involves using results that are readily available.

For example, a computer software store conducts a marketing study by interviewing potential customers who happen to be in the store browsing through the available software. The results of convenience sampling may be very good in some cases and highly biased (favor certain outcomes) in others. Sampling data should be done very carefully. Collecting data carelessly can have devastating results.

Activity 4

Question

Which of the following sampling scenarios describe convenience sampling?

Activity 5

Question

Types of Sampling

Types of Sampling

A random sample is one in which each individual in the population has an equal chance of being selected for the sample. A simple random sample is a sample selected from a population in a way such that all combinations of members of the population of that size have the same chance of being selected.

This video will define and contextualize sampling methods, including convenience sampling, systematic sampling, cluster sampling, and stratified sampling.

Activity 6

Question

Annie wants to estimate the average number of AP classes a student at her high school takes. She decides to randomly select 6 classes and use all the students in those 6 classes to estimate the average.

What type of sampling did Annie use?

Activity 7

Question

Sneha wants to inspect the cleanliness of the rooms in a hotel. There are 10 floors in the hotel and each floor has 20 rooms. From each floor, she randomly selects 2 rooms and inspects them.

What type of sampling did Sneha use?

Activity 8

Question

Identify and Distinguish Between Stratified, Cluster, Systematic, and Convenience Sampling

Types of Sampling

A sample should have the same characteristics as the population it is representing. Most statisticians use various methods of random sampling in an attempt to achieve this goal. There are several different methods of random sampling. In each form of random sampling, each member of a population initially has an equal chance of being selected for the sample.

A simple random sample is a sample selected from a population in a way such that all combinations of members of the population of that size have the same chance of being selected. However, a true simple random sample can sometimes be difficult to obtain. Additionally, researchers may sometimes wish to ensure that some distinguishable characteristic of members in the population is not overrepresented or underrepresented in their sample, as could occur by chance with a simple random sample. Beyond simple random sampling, well-known random sampling methods include stratified sampling, cluster sampling, and systematic sampling.

To choose a stratified sample, you should divide the population into groups, and then take your sample from a proportionate number from each group.

Example

To choose a stratified sample of all students at your college, you could group all the students by the schools they belong to – Liberal Arts, Engineering, Journalism, or Business. To choose a simple random sample from each school, you could number each student in the Liberal Arts school, number each student in the Engineering school, and do the same for the remaining schools.

Then you would randomly choose a proportionate number of students from the Liberal Arts school, the Engineering school, the Journalism school, and the Business school. The combination of all students randomly chosen from each of these schools is the stratified sample.

To choose a cluster sample, divide the population into groups, and then randomly select some of the groups. All the members from these chosen groups are in the cluster sample.

Example

To choose a cluster sample of all students at your college, you could cluster all the students into their majors. You could number these majors (clusters), and then randomly choose five majors using simple random sampling. All students from these five majors make up the cluster sample.

To choose a systematic sample, randomly select a starting point and take every nth piece of data from a listing of the population. Systematic sampling is frequently chosen because it is a simple method.

Example

Suppose you have to do a phone survey, and you want a systematic sample. Your phone book contains 20,000 residence listings. You must choose 400 names for the sample. Number the population 1–20,000 and then use a simple random sample to pick a number that represents the first name in the sample. Then choose every 15th name thereafter until you have a total of 400 names. (You might have to go back to the beginning of your phone list.) Every person in that list of 400 names is in the systematic sample.

Activity 9

Question

True or False? Stratified sampling was used in the scenario below.

A random number generator is used to select a student from the alphabetical listing of all undergraduate students in the Fall semester. Starting with that student, every 50th student is chosen until 75 students are included in the sample.

Activity 10

Question

Identify and Distinguish Between Stratified, Cluster, Systematic, and Convenience Sampling

Convenience Sampling

A type of sampling that is not random is convenience sampling. (Stratified, cluster and systematic sampling are all random.) Convenience sampling involves using results that are readily available.

For example, a computer software store conducts a marketing study by interviewing potential customers who happen to be in the store browsing through the available software. The results of convenience sampling may be very good in some cases and highly biased (favor certain outcomes) in others. Sampling data should be done very carefully. Collecting data carelessly can have devastating results.

Activity 11

Question

Which of the following sampling scenarios describe convenience sampling?

Activity 12

Question

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 voter, they decide to count voters leaving the polling location and ask every 20th voter for an interview. What type of sampling is this?

Activity 13

Question

A professor is interested in the average length of books in her library. She has divided her books into a few different categories: 235 books 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 books. How many sportsbooks should she choose? Enter a whole number.

Activity 14

Question

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 used?

Activity 15

Question

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.

Activity 16

Question

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?

Activity 17

Question

An executive for a large national restaurant chain with multiple locations in each of 513 counties 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?

Activity 18

Question

When is cluster sampling appropriate?

Activity 19

Question

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 households. She plans to use a stratified sampling method. What number of households should be chosen from ward B? Enter a whole number.