Random Sampling And Representativeness Quiz

1) Which plan is most likely to produce a sample with coverage bias?

Plan A

Plan B

Plan C

Plan D

Plan A uses only newsletter subscribers → coverage bias.

Explanation

Plan A uses only newsletter subscribers → coverage bias.

2) A district wants estimates for each school and overall. Best sampling plan?

Stratified random sampling by school

Convenience sample

Simple random sample without labels

Voluntary website survey

Stratifying gives school-level + overall estimates.

Explanation

Stratifying gives school-level + overall estimates.

3) A surveyor randomly selects 100 households but only 40 respond. What reduces nonresponse bias?

Report as is

Replace with neighbors

Follow up via multiple contact modes

Reduce sample size

Follow-ups increase response rate.

Explanation

Follow-ups increase response rate.

4) Two students each take a simple random sample of 50 students and get means 22 and 26 minutes. Best interpretation?

Sampling variability causes differences

One sampled incorrectly

Larger number is more accurate

Should use convenience sampling

Different random samples differ slightly.

Explanation

Different random samples differ slightly.

5) In which situation is a convenience sample acceptable?

Estimating district-wide graduation rate

Making policy decisions

Estimating voter preferences

Conducting a quick classroom poll

Convenience sampling okay when not generalizing.

Explanation

Convenience sampling okay when not generalizing.

6) A school posts a survey on the website. Biggest concern?

Coverage bias

Voluntary response bias

Response bias

Systematic error

Self-selected participation → voluntary response bias.

Explanation

Self-selected participation → voluntary response bias.

7) A teacher wants to estimate the fraction of students who prefer project-based assessments. Which method is stratified sampling?

Randomly select 60 students from the entire school

Ask the first 80 entering cafeteria

Randomly select 20 students from each grade level

Survey all AP students

Stratified = sample within each grade.

Explanation

Stratified = sample within each grade.

8) Which plan best reduces sampling variability for neighborhood-level estimates?

Plan A

Plan B

Plan C

Plan D

Stratified sampling reduces variability.

Explanation

Stratified sampling reduces variability.

9) Which plan is most strongly affected by voluntary response bias?

Plan A

Plan B

Plan C

Plan D

Plan C uses volunteers at a festival → voluntary response.

Explanation

Plan C uses volunteers at a festival → voluntary response.

10) Which plan is most likely to be both random and representative across neighborhoods?

Plan A

Plan B

Plan C

Plan D

Plan D uses stratified sampling by neighborhood.

Explanation

Plan D uses stratified sampling by neighborhood.

11) A school wants to estimate the average number of hours students spend on homework per night. Which sampling method is most likely to produce a representative sample?

Using a random number generator to select 100 students from the full student roster

Surveying students in the library after school

Posting a survey link in the honors classes group chat

Asking teachers to choose students they think are average

A random number generator gives a random sample of students from the whole school, making it more representative.

Explanation

A random number generator gives a random sample of students from the whole school, making it more representative.

12) In a school of 1,200 students, a simple random sample of 60 is chosen. Which statement is true about sampling variability?

It guarantees the sample average equals the population average

Sampling variability disappears when random

Different random samples of 60 give slightly different estimates

It only matters when sample < 30

Random samples differ slightly due to sampling variability.

Explanation

Random samples differ slightly due to sampling variability.

13) A survey asks, “Do you agree that the excellent new policy should continue?” What issue is most present?

Coverage bias

Sampling variability

Randomization error

Leading question bias

Word 'excellent' leads respondents.

Explanation

Word 'excellent' leads respondents.

14) A researcher selects every 10th student entering the school after a randomly chosen starting point. What sampling method is this?

Simple random sampling

Convenience sampling

Systematic random sampling

Stratified sampling

Every kth after random start = systematic sampling.

Explanation

Every kth after random start = systematic sampling.

15) You want to minimize sampling variability. Which helps most?

Use convenience sample

Only include top students

Cluster students by class

Increase random sample size

Larger random sample reduces variability.

Explanation

Larger random sample reduces variability.

16) A district wants to estimate the percentage of parents satisfied with school lunches. Which plan is most likely to yield a random sample?

Randomly selecting parent emails from full contact list

Sending survey to PTA attendees

Posting the survey on social media

Asking cafeteria staff to distribute surveys

Random selection from full list gives fair chance.

Explanation

Random selection from full list gives fair chance.

17) Which method best reduces nonresponse bias in a mailed survey?

Making the survey longer

Following up with reminders and incentives

Only surveying people who replied within 24 hours

Asking people to share the survey with friends

Reminders/incentives improve response rates.

Explanation

Reminders/incentives improve response rates.

18) A survey is sent only to students with school email addresses ending in “honors.school.org.” What type of bias is most likely introduced?

Nonresponse bias

Response bias

Coverage bias

Voluntary response bias

Only honors students are covered; others excluded → coverage bias.

Explanation

Only honors students are covered; others excluded → coverage bias.

19) A student claims that a sample of 30 randomly selected students is “too small to be random.” What is the best response?

A sample must be at least 100 to be random

Randomness is about the selection process, not the size

A sample is random only if it contains at least 10% of the population

A random sample requires equal numbers from each grade

Randomness is about selection method, not size.

Explanation

Randomness is about selection method, not size.

20) Which scenario best describes a biased sample?

Randomly selecting 50 students from the entire student database

Assigning each student an ID and selecting a random subset

Surveying only students attending the math club meeting

Using a lottery to select students from all grade levels

Only math club students are surveyed, so students who like math more are overrepresented → biased.

Explanation

Only math club students are surveyed, so students who like math more are overrepresented → biased.

Random Sampling and Representativeness Quiz

1) Which plan is most likely to produce a sample with coverage bias?

2)

What first name or nickname would you like us to use?

2) A district wants estimates for each school and overall. Best sampling plan?

3) A surveyor randomly selects 100 households but only 40 respond. What reduces nonresponse bias?

4) Two students each take a simple random sample of 50 students and get means 22 and 26 minutes. Best interpretation?

5) In which situation is a convenience sample acceptable?

6) A school posts a survey on the website. Biggest concern?

7) A teacher wants to estimate the fraction of students who prefer project-based assessments. Which method is stratified sampling?

8) Which plan best reduces sampling variability for neighborhood-level estimates?

9) Which plan is most strongly affected by voluntary response bias?

10) Which plan is most likely to be both random and representative across neighborhoods?

11) A school wants to estimate the average number of hours students spend on homework per night. Which sampling method is most likely to produce a representative sample?

12) In a school of 1,200 students, a simple random sample of 60 is chosen. Which statement is true about sampling variability?

13) A survey asks, “Do you agree that the excellent new policy should continue?” What issue is most present?

14) A researcher selects every 10th student entering the school after a randomly chosen starting point. What sampling method is this?

15) You want to minimize sampling variability. Which helps most?

16) A district wants to estimate the percentage of parents satisfied with school lunches. Which plan is most likely to yield a random sample?

17) Which method best reduces nonresponse bias in a mailed survey?

18) A survey is sent only to students with school email addresses ending in “honors.school.org.” What type of bias is most likely introduced?

19) A student claims that a sample of 30 randomly selected students is “too small to be random.” What is the best response?

20) Which scenario best describes a biased sample?