AP Stats Experimental Design 2 — Questions and Answers
Question 1: A researcher wants to test whether a new fertilizer increases crop yield. She randomly assigns 40 plots to fertilizer and 40 plots to no fertilizer. What is the primary purpose of random assignment in this experiment?
- To ensure the sample is representative of all farms
- To create equivalent groups and allow causal inference (Correct answer)
- To reduce measurement error in crop yield
- To increase the number of experimental units
Correct answer: To create equivalent groups and allow causal inference
Random assignment balances confounding variables across treatment groups, enabling valid causal conclusions.
Question 2: In a study on pain relief, neither patients nor doctors know who received the actual medication. This design feature is called:
- Single-blind
- Double-blind (Correct answer)
- Placebo-controlled
- Matched pairs
Correct answer: Double-blind
Double-blind means both subjects and evaluators are unaware of treatment assignment, reducing bias from both sides.
Question 3: A school district tests a new math curriculum in 5 classrooms while 5 others use the old curriculum. Students were not randomly assigned to classrooms. This study is best described as:
- A randomized experiment
- A matched pairs experiment
- An observational study (Correct answer)
- A quasi-experiment
Correct answer: An observational study
Without random assignment of subjects to treatments, the study is observational and cannot establish causation.
Question 4: Which of the following is an example of a lurking variable?
- The treatment variable deliberately manipulated by the researcher
- A variable measured as the response in the study
- An unmeasured variable that affects both the explanatory and response variables (Correct answer)
- A blocking variable used to control variation
Correct answer: An unmeasured variable that affects both the explanatory and response variables
A lurking variable is not measured but influences both the explanatory and response variables, potentially confounding results.
Question 5: Researchers block by gender before randomly assigning participants to treatment groups. The main reason for blocking is to:
- Increase the total sample size
- Reduce variation within treatment groups by accounting for a known source of variability (Correct answer)
- Prevent participants from knowing their treatment
- Ensure equal numbers in each treatment group overall
Correct answer: Reduce variation within treatment groups by accounting for a known source of variability
Blocking groups similar experimental units together so that variation due to the blocking variable does not obscure treatment effects.
Question 6: In a completely randomized design with three treatments, 60 subjects are randomly assigned so that each treatment group has 20 subjects. What is the key advantage of this design over a block design?
- It eliminates all confounding variables
- It is simpler to implement when no major sources of variation are known (Correct answer)
- It always produces more statistically significant results
- It requires fewer subjects than a block design
Correct answer: It is simpler to implement when no major sources of variation are known
A completely randomized design is appropriate and simpler when no important blocking variables are identified.
Question 7: A researcher uses a table of random digits to assign subjects to treatment groups. Subject 1 gets the first digit, subject 2 gets the second, etc., assigning odd digits to Treatment A and even digits to Treatment B. This procedure ensures:
- Stratified sampling
- Systematic sampling
- Random assignment to treatments (Correct answer)
- Convenience sampling
Correct answer: Random assignment to treatments
Using a random digit table to assign subjects to treatments is a valid method of random assignment in an experiment.
AP Stats Experimental Design 2
A researcher wants to test whether a new fertilizer increases crop yield.
She randomly assigns 40 plots to fertilizer and 40 plots to no fertilizer.
What is the primary purpose of random assignment in this experiment?