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AP Statistics 1.13 Experimental Design- Exam Style Questions - MCQs - New Syllabus

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Question

Professor A and Professor Z wish to study the relationship between coffee drinking and exam performance in their large lecture classes at a small college in Massachusetts. They approach their data collection differently:

  • Professor A gives an exam to the entire class. At the start of the exam, after asking for the student’s name, the exam asks the questions: “Have you drank any coffee today? If so, approximately how much?”
  • Professor Z, a few days before the exam, selects ½ of his students at random. These students receive a gift card to a campus coffee shop and are told that they must drink at least one coffee drink before the exam. The other half of the class does not receive a free gift card and are instructed not to drink any coffee before the exam.

After the exams are completed, both Professors analyze their exam results to determine if there is a relationship between coffee drinking and exam performance. Which of the following statements is true?

(A) Since both professors are asking the students to complete a task, both are performing a controlled experiment.
(B) Any relationship these professors uncover between coffee drinking and exam performance applies to the entire population of Massachusetts.
(C) The population of interest for each of these professors is all coffee drinkers.
(D) Professor A is running an observational study, and Professor Z is running a controlled experiment.
(E) The biggest weakness of Professor A’s research is undercoverage, while the most glaring concern of Professor Z’s research is nonresponse bias.

▶️ Answer/Explanation

Professor A simply records whether students consumed coffee and then compares that information to exam performance. Since no treatment is imposed, this is an observational study.

Professor Z randomly assigns students to drink coffee or avoid coffee before the exam. Because a treatment is imposed and random assignment is used, this is a controlled experiment.

The distinction between observing existing behavior and assigning treatments is fundamental in statistical study design. Therefore, choice (D) correctly describes the two approaches.
✅ Answer: (D)

Question 

A veterinarian designs an experiment to determine whether a new flea medication will work better than the current medication he commonly prescribes for animals. The veterinarian identifies a group of dogs that are currently infested with fleas. She randomly assigns the dogs to receive either the new medication or to receive the current medication. She finds that the proportion of surviving fleas on the dogs that took the new medication is significantly lower than the proportion of surviving fleas on the dogs that took the current medication. The veterinarian concludes that the new medication is better at killing fleas on animals. Is this the correct conclusion?

(A) No, because there was not a group that received a placebo.
(B) No, because the experiment was only done with dogs so the results cannot be generalized to all animals with fleas.
(C) Yes, because the dogs were randomly assigned to the two treatment groups.
(D) Yes, because the proportion of surviving fleas was significantly lower for the new medication.
(E) Yes, because there was a control group to reduce the effects of any lurking variables.

▶️ Answer/Explanation

The experiment was conducted only on dogs, yet the veterinarian’s conclusion was extended to all animals. While random assignment allows a cause-and-effect conclusion for the dogs in the experiment, it does not justify generalizing the results to other types of animals.

A study can only be generalized to the population from which the subjects were drawn. Since the sample consisted exclusively of dogs, the conclusion should be limited to dogs with fleas rather than all animals with fleas.

Therefore, the veterinarian’s conclusion is not fully justified.
✅ Answer: (B)

Question 

Some wood products are treated with chemicals to make them last longer, resist rot, and stand up to weather. A company is testing two different chemical mixtures, Green and Brown, to treat their wood products. They are interested in knowing which mixture is more easily absorbed by wood.

The scientists collect 40 pieces of the same type of wood, all with the same dimensions. The scientists select the two heaviest pieces and randomly assign one of the pieces to receive the Green mixture and one the Brown mixture. They then pick the next two heaviest pieces and randomly assign one of these to receive the Green mixture and one the Brown mixture. They repeat this until all the pieces have been assigned. Each piece of wood is measured to determine the amount of mixture absorbed. This study uses which of the following?

(A) Cluster Sampling
(B) Systematic Sampling
(C) A completely randomized design
(D) A matched pair design
(E) A randomized block, but not matched pairs

▶️ Answer/Explanation

The researchers first group together two wood pieces with very similar weights (the two heaviest, the next two heaviest, and so on). Within each pair, one piece is randomly assigned to the Green mixture and the other to the Brown mixture.

This creates pairs of similar experimental units before treatment assignment. Since each pair contains two closely matched pieces and both treatments are represented within every pair, the design is a matched pairs experiment, which is a special type of randomized block design.

The key feature is that the blocking is done using pairs of nearly identical wood pieces.

✅ Answer: (D)

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