Question 1

Use the following information for questions:
 Olivia wants to learn a foreign language. To get an idea of how satisfied other students were after taking a foreign language course, she decides to take a random sample of 20 students.
-If Olivia randomly selects 5 students from French, 5 from German, 5 from Spanish, and 5 from Chinese, the sampling method is a
A) simple random sample.
B) stratified random sample.
C) cluster sample.
D) systematic sample.

Accepted Answer

Olivia's method is a stratified random sample because she divides the population into groups (strata) based on the language and then takes a random sample from each group.

Question 2

Use the following information for questions:
 Olivia wants to learn a foreign language. To get an idea of how satisfied other students were after taking a foreign language course, she decides to take a random sample of 20 students.
-If Olivia randomly selects one class among all the foreign language classes taught that year, and then interviews all students in that class, the sampling method is a
A) simple random sample.
B) stratified random sample.
C) cluster sample.
D) systematic sample.

Accepted Answer

Cluster sampling involves selecting entire groups or clusters where every member of the selected group is surveyed. In this case, Olivia selects one class (a cluster) and interviews all students in that class, which aligns with the definition of cluster sampling.

Question 3

Use the following information for questions:
 Olivia wants to learn a foreign language. To get an idea of how satisfied other students were after taking a foreign language course, she decides to take a random sample of 20 students.
-If Olivia randomly selects 20 students among all students taking a foreign language class that year, the sampling method is a
A) simple random sample.
B) stratified random sample.
C) cluster sample.
D) systematic sample.

Accepted Answer

Olivia's method of randomly selecting 20 students from all students taking a foreign language class without any specific grouping or order is a definition of a simple random sample.

Question 4

Use the following information for questions: Olivia wants to learn a foreign language. To get an idea of how satisfied other students were after taking a foreign language course, she decides to take a random sample of 20 students. -If Olivia selects every 100^th student from a list of the 2000 students who took a foreign language that year, the sampling method is a A) simple random sample. B) stratified random sample. C) cluster sample. D) systematic sample.

Accepted Answer

Olivia's method of selecting every 100th student from a list of 2000 students is a systematic sampling method, where a sample is drawn by selecting a starting point at random and then picking every nth element in succession from the list.

Question 5

A magazine printed a survey in its monthly issue and asked readers to fill it out and send it in. Over 1000 readers did so. This type of sample is called a
A) cluster sample.
B) stratified sample.
C) simple random sample.
D) self-selected sample.

Accepted Answer

This is a self-selected sample because the respondents chose themselves to participate by filling out and sending in the survey, rather than being randomly selected by the researchers.

Question 6

A population of taxpayers is divided into five income levels and a simple random sample is selected from each one for an audit. This is an example of a _________ sample.
A) cluster
B) stratified
C) simple random
D) systematic

Accepted Answer

This is an example of a stratified sample because the population is divided into distinct subgroups (strata) based on income levels, and then a simple random sample is selected from each subgroup.

Question 7

Taxpayers in a population are listed in order of increasing income, with people with the lowest incomes listed first. A sample is selected by randomly choosing one of the first 100 names, then choosing every 100^th name from that point forward. This is an example of a __________ sample. A) stratified B) cluster C) simple random D) systematic

Accepted Answer

This is an example of a systematic sample because it involves selecting a sample by choosing a starting point at random and then selecting every kth element in the population from that point on.

Question 8

Children at a Kindergarten school are divided into three groups: Those who are the oldest/first child (there are 200 of them, call this Group I), those who are the second child (there are 150, call this Group II), and those who are the third (or even fourth or fifth) child (there are 75, call this Group III). The social worker at the school will take a sample to find out how many sleepovers they have had (without parents) at a friend's house. She suspects that first-borns do not get as many as later children, so she decides to take a simple random sample of 15 children from each of the three groups. What sampling technique will be used to obtain the sample of children?
A) stratified
B) cluster
C) simple random
D) multi-stage

Accepted Answer

The social worker is using a stratified sampling technique because she divides the population into distinct groups (strata) based on a specific characteristic (birth order) and then takes a simple random sample from each of these groups.

Question 9

A librarian wants to gather data on the number of times books of fiction are checked out during the year. The library has 2000 books of fiction, of which 500 are murder mysteries, 400 are science fiction, and the rest are "other". She decides to sample 120 books. Suppose the librarian decides to take a simple random sample of 30 books from the murder mystery category, 24 from the science fiction category, and the remaining 66 from the other category. What sampling technique was used?
A) simple random
B) cluster
C) stratified
D) multi-stage

Accepted Answer

The librarian used stratified sampling because she divided the books into distinct categories (strata) - murder mysteries, science fiction, and others - and then took a sample from each category.

Question 10

A company that produces electronics (stereos, TV's, DVD players, etc.) is thinking about adding an incentive program to the contracts of its employees. To learn about the opinion of its employees regarding this idea, a survey will be sent out to a sample of the employees. To ensure that employees of all three plants are represented in the survey, the statistician decides to take a sample of employees from each of the three plants. At each plant, a list is available of all employees. A 1-in-20 systematic sample will be taken from each plant. What sampling technique is being used to sample the employees?
A) simple random
B) cluster
C) stratified
D) multi-stage

Accepted Answer

The answer of A company that produces electronics (stereos, TV's,...

Question 11

Use the following information for questions:
 The Michigan Department of State Police keeps track of the number of points received for various traffic violations by Michigan drivers. The department is interested in examining the relationship between the number of points received and the insurance premium. The following chart shows the number of drivers in each category of points according to the records from last year.  The department will take a simple random sample of 3% of the drivers in the Low category and 2% of the drivers in the other two categories.
-How many drivers will be included in the study?
A) 574
B) 24
C) 540
D) 399

Accepted Answer

The study will include 574 drivers.

Question 12

Use the following information for questions:
 The Michigan Department of State Police keeps track of the number of points received for various traffic violations by Michigan drivers. The department is interested in examining the relationship between the number of points received and the insurance premium. The following chart shows the number of drivers in each category of points according to the records from last year.  The department will take a simple random sample of 3% of the drivers in the Low category and 2% of the drivers in the other two categories.
-What sampling method will be used to obtain the sample?
A) simple random
B) cluster
C) stratified
D) multi-stage

Accepted Answer

Stratified sampling is used when the population is divided into different subgroups or 'strata' that are distinct from one another, and samples are drawn from each of these subgroups. This method ensures representation from all subgroups within the population, which is not specified in the question but is implied by the selection of stratified sampling as the correct answer.

Question 13

There are five cities in a politician's district but redistricting has been proposed for the state. The politician would like to know which city he should try to remove from his district. He plans to conduct a survey to find out his approval rating. Which one of the following sampling plans would be most useful for his purposes?
A) Take a stratified sample with political parties as the strata.
B) Take a stratified sample with the five cities as the strata.
C) Take a simple random sample across his district.
D) Take a cluster sample with the five cities as clusters.

Accepted Answer

Taking a stratified sample with the five cities as the strata would allow the politician to accurately assess his approval rating in each city individually, helping him decide which city to remove from his district based on lower approval ratings.

Question 14

Which of the following is the best example of a population from which a cluster sample would be easier to obtain that a simple random sample?
A) Passengers who will be flying in the upcoming week on a certain airline.
B) Registered drivers in a certain state.
C) Employees of a large company.
D) Members of a national organization.

Accepted Answer

Cluster sampling involves dividing the population into separate groups, or clusters, and then a simple random sample of these clusters is selected. If the population is passengers flying on a certain airline in the upcoming week, it's easier to divide this population into clusters (e.g., flights) and then randomly select a few flights to survey all passengers on those flights, compared to trying to randomly select individual passengers across all flights.

Question 15

One problem with using random digit dialing to get a representative sample of households in a city is that
A) the method can only be used to get a sample for the whole country.
B) households with multiple telephones on the same line will be over-represented.
C) households with multiple phone numbers will be over-represented.
D) households with unlisted phone numbers will not be represented.

Accepted Answer

Households with multiple phone numbers have a higher chance of being selected, leading to over-representation in the sample.

Question 16

Use the following information for questions:
 These questions pertain to how to collect a random sample of 800 airline passengers from 100 particular flights leaving San Francisco International Airport. Assume there are 200 passengers aboard each flight.
-Describe how to draw the sample as a stratified random sample, using the 100 flights as the strata.

Accepted Answer

The answer of Use the following information for questions:
 These...

Question 17

Use the following information for questions:
 These questions pertain to how to collect a random sample of 800 airline passengers from 100 particular flights leaving San Francisco International Airport. Assume there are 200 passengers aboard each flight.
-Describe how to draw the sample as a cluster random sample, using flights as the cluster.

Accepted Answer

The answer of Use the following information for questions:
 These...

Question 18

Use the following information for questions:
 These questions pertain to how to collect a random sample of 800 airline passengers from 100 particular flights leaving San Francisco International Airport. Assume there are 200 passengers aboard each flight.
-Describe how to draw the sample as a systematic sample from these flights.

Accepted Answer

The answer of Use the following information for questions:
 These...

Question 19

Both cluster and stratified sampling rely on sub-groups in the population. If the sub-groups are all very similar (they can all be considered mini-populations), which sampling method would be preferred?

Accepted Answer

The answer of Both cluster and stratified sampling rely on...

Question 20

On a chilly spring afternoon, 10 lab sections of a statistics class all have full attendance. The 10 lab sections each have the same number of students attending. A survey is about to be administered to a sample of the students. It has been decided to first randomly select 3 of the 10 lab sections and then give the evaluation to a simple random sample of 25% of the students in those selected lab sections. What sampling technique is being used for this survey?

Accepted Answer

The answer of On a chilly spring afternoon, 10 lab...

Quiz 5: Sampling: Surveys and How to Ask Questions

A magazine printed a survey in its monthly issue and asked readers to fill it out and send it in. Over 1000 readers did so. This type of sample is called a

A population of taxpayers is divided into five income levels and a simple random sample is selected from each one for an audit. This is an example of a _________ sample.

Taxpayers in a population are listed in order of increasing income, with people with the lowest incomes listed first. A sample is selected by randomly choosing one of the first 100 names, then choosing every 100th name from that point forward. This is an example of a __________ sample.

Which of the following is the best example of a population from which a cluster sample would be easier to obtain that a simple random sample?

One problem with using random digit dialing to get a representative sample of households in a city is that

Both cluster and stratified sampling rely on sub-groups in the population. If the sub-groups are all very similar (they can all be considered mini-populations), which sampling method would be preferred?

Taxpayers in a population are listed in order of increasing income, with people with the lowest incomes listed first. A sample is selected by randomly choosing one of the first 100 names, then choosing every 100^th name from that point forward. This is an example of a __________ sample.