Question

athletes who had suffered broken legs were randomly assigned to one of two exercise programs. the first group returned to sports activities in a mean of 60.7 days (with a standard deviation of 28.5 days). the other group returned to sports in a mean of 51 days (with a standard deviation of 10.7 days).
a) explain why it was important to assign the athletes to the two different treatments randomly.
a. allowing the athletes to choose their own treatments could confound the results.
b. the treatments were assigned randomly so that the negative effects of working out with friends could be neglected.
c. the treatments were assigned randomly so that the positive effects of working out with friends could be neglected.
b) there was no control group of athletes who did not participate in a special exercise program. explain the advantage of including such a group in this experiment.
a. a control group could have revealed whether either exercise program was better or worse than just letting the injury heal without exercise.
b. a control group could have revealed why one program was more successful at healing the injury than the other.
c. a control group could have revealed whether participating in both exercise programs was better or worse than participating in only one.

Explanation:

Part (a)

To determine the correct option for why random assignment was important:

• Option A: If athletes chose their own treatments, factors like their motivation, injury severity perception could confound results (e.g., more motivated athletes choosing a program, biasing results). Random assignment balances such factors.
• Option B: The study is about exercise programs for broken legs, not working out with friends. So this is irrelevant.
• Option C: Similar to B, the study isn't about working out with friends, so this is incorrect.

So the correct option is A.

To determine the correct option for the advantage of a control group:

• Option A: A control group (athletes not in any exercise program) would let us compare the exercise programs' effects to natural healing (no exercise). This is the purpose of a control group in an experiment testing treatments.
• Option B: A control group doesn't explain why one program is better than the other (that's about comparing the two treatment groups, not a control).
• Option C: The study is about two separate programs, not combining them. So this is irrelevant.

So the correct option is A.

Answer:

A. Allowing the athletes to choose their own treatments could confound the results.

Part (b)