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Difficulty: HardStatistical Sampling and Studies

A researcher wants to investigate the relationship between regular exercise and resting heart rate for adults residing in a certain city. The researcher obtains a list of all registered members of a large local fitness center and randomly selects 250 of these members to participate in a study. The study finds a strong negative correlation: members who reported exercising more than 5 hours per week had, on average, a significantly lower resting heart rate than those who reported exercising less than 5 hours per week. Which of the following is the most appropriate conclusion to draw from this study?

  1. A
    Exercising more than 5 hours per week causes a lower resting heart rate for all adults residing in the city.
  2. B
    Exercising more than 5 hours per week causes a lower resting heart rate for the members of this fitness center.
  3. There is an association between exercising more than 5 hours per week and having a lower resting heart rate for the members of this fitness center, but a causal relationship cannot be established.Answer
  4. D
    There is an association between exercising more than 5 hours per week and having a lower resting heart rate for all adults residing in the city, but a causal relationship cannot be established.

Answer

There is an association between exercising more than 5 hours per week and having a lower resting heart rate for the members of this fitness center, but a causal relationship cannot be established.
The correct answer is the statement concluding that there is an association for the members of this fitness center, but a causal relationship cannot be established. Since the sample was randomly selected from the registered members of the local fitness center, the findings can be generalized to that population. However, because this is an observational study (no random assignment to exercise groups), a causal relationship cannot be established.

Step-by-Step Solution

1
Determine the target population that the sample represents.
The sample of 250 members was randomly selected from the registered members of a specific local fitness center.
Results of a statistical study can only be generalized to the population from which the sample was randomly selected. Because fitness center members are not representative of all adults in the city, the findings cannot be generalized to the entire city.
2
Evaluate the nature of the study design to check if causal conclusions can be made.
The study is observational because the researcher did not randomly assign participants to different exercise levels; the participants merely reported their existing habits.
A cause-and-effect relationship can only be established through a randomized controlled experiment. Observational studies can show association (correlation) but cannot establish causation.
3
Combine the limitations of generalization and causation to select the correct conclusion.
The study can only conclude that there is an association between exercise and resting heart rate for the members of this fitness center, with no causal claims allowed.
This is the only conclusion that respects both the sampling method and the observational design of the study.

Key Concept

Generalization and Causal Inference in Statistical Studies
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Topics

Statistical Sampling and Studies

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