AP Statistics 3.7 Inference and Experiments- MCQs - Exam Style Questions

Question

To investigate whether the consumption of beetroot juice enhances exercise performance, a researcher selected a random sample of \(50\) student athletes from all the student athletes at a college. The athletes in the sample were randomly assigned to one of two groups. In one group, \(25\) athletes were given a daily dose of beetroot juice, and in the other group, the remaining athletes were given a daily dose of a placebo. At the end of six weeks of exercise training, the researcher compared the performances of the two groups. Based on the design of the investigation, which of the following is the largest population to which the results can be generalized?

(A) The \(25\) student athletes assigned to the beetroot juice group
(B) The \(50\) student athletes in the sample
(C) All student athletes at the college
(D) All students at the college
(E) All people who exercise

▶️ Answer/Explanation

Detailed solution

Results can be generalized to the population from which the sample was randomly selected. Here, the random sample was drawn from all student athletes at the college. Random assignment allows causal conclusions within the sample but does not expand the scope of generalization beyond the sampling frame.
Therefore, the largest population supported by the design is all student athletes at the college.
✅ Answer: (C)

(A) Only a treatment group subset — too narrow.
(B) The sample itself — not a population for generalization.
(D) Includes non-athletes — outside the sampling frame.
(E) Includes people not from the college — outside the sampling frame.

Question

Researchers conducted a study to investigate the effects of soft drink consumption on fat stored in muscle tissue. From a sample of 80 adult volunteers, 40 were randomly assigned to consume one liter of a soft drink each day. The remaining 40 were asked to drink one liter of water each day and not to consume any soft drinks. At the end of six months, the amount of fat stored in each person’s muscle tissue was recorded. The people in the group who drank the soft drink had, on average, a higher percentage of fat stored in the tissue than the people who drank only water.

Which of the following is the most appropriate conclusion?

(A) There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only water, and the conclusion can be generalized to all adults.
(B) There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only water, and the conclusion can be generalized to all people who consume soft drinks.
(C) There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only water, and the conclusion can be generalized to adults similar to those in the study.
(D) Although cause-and-effect cannot be established, there is an association between consuming soft drinks and fat storage in muscle tissue for the population of all adults.
(E) Although cause-and-effect cannot be established, there is an association between consuming soft drinks and fat storage in muscle tissue for the population of all adults who consume soft drinks.

▶️ Answer/Explanation

Detailed solution

1. Causation vs. Association:
The study used random assignment to place volunteers into the two groups (soft drink vs. water). This experimental design controls for confounding variables and allows for making a cause-and-effect conclusion. Therefore, we can infer causation, which eliminates options (D) and (E).

2. Generalizability:
The subjects in the study were volunteers, not a random sample from a larger population. Because there was no random sampling, the results cannot be generalized to “all adults.” Instead, the conclusions are limited to the type of people who would volunteer for such a study, described as “adults similar to those in the study.”

✅ Answer: (C)

AP Statistics 3.7 Inference and Experiments- MCQs - Exam Style Questions

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