AP Stats Sampling Methods and Design 3 — Questions and Answers
Question 1: A study finds that students who eat breakfast score higher on exams. A lurking variable that could explain this relationship is:
- The type of breakfast food consumed
- Socioeconomic status of the family (Correct answer)
- The difficulty of the exam
- The number of questions on the test
Correct answer: Socioeconomic status of the family
Socioeconomic status affects both the ability to regularly eat breakfast and access to educational resources that improve exam scores.
Question 2: The difference between an observational study and an experiment is that in an experiment:
- The sample size must be larger
- The researcher actively imposes treatments on subjects (Correct answer)
- All variables are controlled and measured
- Random sampling is required
Correct answer: The researcher actively imposes treatments on subjects
In an experiment, the researcher deliberately assigns treatments to subjects, whereas an observational study merely records existing conditions.
Question 3: A survey asks: 'Do you agree that the government wastes taxpayer money?' This question suffers from:
- Undercoverage bias
- Non-response bias
- Leading question bias (Correct answer)
- Sampling frame error
Correct answer: Leading question bias
The wording 'Do you agree that' steers respondents toward agreement, introducing leading question bias that inflates 'yes' responses.
Question 4: In a completely randomized design, the purpose of random assignment is to:
- Increase the sample size needed
- Ensure the sample represents the population
- Balance confounding variables across treatment groups on average (Correct answer)
- Eliminate measurement error
Correct answer: Balance confounding variables across treatment groups on average
Random assignment distributes both known and unknown confounding variables roughly equally among groups, allowing causal conclusions.
Question 5: A researcher surveys shoppers leaving a grocery store on a Tuesday morning. This is an example of:
- Systematic sampling
- Cluster sampling
- Convenience sampling (Correct answer)
- Stratified sampling
Correct answer: Convenience sampling
Selecting whoever is easily available (shoppers present at that specific time and place) is convenience sampling, which is prone to undercoverage bias.
Question 6: When using a random number table to select a simple random sample of 5 from 80 students numbered 01–80, you should:
- Use one-digit numbers and ignore 0 and 9
- Use two-digit numbers and skip those outside 01–80 (Correct answer)
- Use two-digit numbers and include 00 as student 80
- Use three-digit numbers to ensure all students have equal probability
Correct answer: Use two-digit numbers and skip those outside 01–80
Students are labeled with two-digit numbers 01–80, so you read two-digit groups and skip any numbers outside that range (81–99 and 00).
Question 7: Which of the following best describes a double-blind experiment?
- Neither subjects nor evaluators know who received which treatment (Correct answer)
- The experimenter does not know the hypothesis being tested
- Subjects are randomly assigned and no placebo is used
- Both a control group and an experimental group are used
Correct answer: Neither subjects nor evaluators know who received which treatment
Double-blind means both the participants and those evaluating outcomes are unaware of treatment assignment, preventing bias from expectations.
AP Stats Sampling Methods and Design 3
A study finds that students who eat breakfast score higher on exams.
A lurking variable that could explain this relationship is: