Q: A department store wants to estimate the proportion of satisfied customers. Out of 51,000 customers, 1500 are randomly selected and surveyed, but only 142 respond. What is the response rate?

$$ \frac{142}{1500} \times 100 \approx 9.47\% $$

Question 1

In the department store customer satisfaction survey, what is the variable or parameter being researched?

Accepted Answer

The satisfaction level of customers who made credit card purchases

Question 2

In the department store survey scenario, which of the following best describes the population of the study?

Accepted Answer

All people who made credit card purchases at the store in the past month

Question 3

What is the sample frame in the department store customer satisfaction survey?

Accepted Answer

The 1500 randomly selected addresses to which the survey was mailed

Question 4

Which of the following best describes the sample in the department store survey?

Accepted Answer

The 142 people who returned the survey

Question 5

Why might the sample of 142 returned surveys NOT be representative of the population in the department store study?

Accepted Answer

Because only those who felt strongly may have responded, introducing nonresponse bias

Question 6

A political science student wants to survey college students about Medicare eligibility. She uses systematic sampling by emailing every 20th student on an alphabetized list. What is a potential source of bias in this method?

Accepted Answer

The order of the list may be related to a variable of interest, leading to bias

Question 7

Which sampling method ensures that every individual in the population has an equal chance of being selected?

Accepted Answer

Simple random sampling (SRS)

Question 8

A sociologist randomly selects 3 high schools in a district and surveys every senior in those schools. What type of sampling is this?

Accepted Answer

Cluster sampling

Question 9

In stratified sampling, which of the following best describes the process?

Accepted Answer

Divide the population into subgroups and randomly sample from each subgroup

Question 10

Suppose a researcher wants to estimate the average GPA of students at a university. She divides students by major and randomly selects 10 students from each major. What sampling method is she using?

Accepted Answer

Stratified sampling

Question 11

If a sample is not representative of the population, which of the following is most likely to occur?

Accepted Answer

The results may be biased and not generalizable to the population

Question 12

A researcher compiles a list of all seniors in a school district and randomly selects 500 seniors from that list. What type of sampling is this?

Accepted Answer

Stratified sampling

Question 13

Which of the following is a key advantage of using a simple random sample (SRS)?

Accepted Answer

It ensures that every individual has an equal chance of being selected

Question 14

A department store wants to estimate the proportion of satisfied customers. Out of 51,000 customers, 1500 are randomly selected and surveyed, but only 142 respond. What is the response rate?

Accepted Answer

$$ \frac{142}{1500} 	imes 100 \approx 9.47\% $$

Question 15

Which of the following best describes nonresponse bias?

Accepted Answer

Bias that occurs when individuals selected for the sample do not respond, and their opinions differ from those who do respond

Question 16

A researcher wants to estimate the average height of high school seniors in a district. She randomly selects 30 seniors from each of the 15 high schools. What sampling method is this?

Accepted Answer

Stratified sampling

Question 17

Which of the following is a potential disadvantage of cluster sampling?

Accepted Answer

Clusters may not be representative of the population, leading to increased sampling error

Question 18

A university wants to survey student opinions on a new policy. Which sampling method would be most appropriate to ensure that students from all years (freshman, sophomore, junior, senior) are included proportionally?

Accepted Answer

Stratified sampling

Question 19

If a researcher uses a simple random sample (SRS) of 190 students from a population of 3,872, what is the probability that any one student is selected?

Accepted Answer

$$ \frac{190}{3872} $$

Sampling Methods and Survey Design in Statistics

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