Question 25·Easy·Evaluate Statistical Claims: Observational Studies and Experiments
To estimate the proportion of adults in a county who regularly exercise, a researcher sets up a booth at the finish line of a local 10-kilometer race and surveys the next 150 finishers about whether they exercise at least 3 times per week. Most respondents answer yes.
Which statement accurately describes the researcher’s survey?
For survey and statistics design questions, first identify the population (who we care about) and the sample (who was actually studied). Then ask whether the sampling method makes the sample representative or introduces bias—for example, by only including volunteers with a special interest or people at a specific event. Also distinguish observational studies (just observing or asking questions) from experiments (imposing treatments). Focus on these definitions and logic rather than on calculations to answer quickly and accurately.
Hints
Clarify population vs. sample
Ask yourself: Who does the researcher want to learn about (the population), and who is actually being surveyed (the sample)?
Think about representativeness
Consider whether people who finish a 10-kilometer race are similar to a typical adult in the county in terms of exercise habits, or whether they might systematically differ.
Distinguish survey from experiment and bias from size
Ask: Did the researcher do anything to the participants besides ask questions (which would make it an experiment)? Also, would simply asking more people from the same situation fix any problem with how the group was chosen?
Step-by-step Explanation
Identify the goal and the population
The researcher wants to estimate the proportion of all adults in the county who regularly exercise (the population). To do that, they collect data from a smaller group (a sample). For the conclusion to be valid, the sample must represent the entire population fairly.
Examine how the sample was selected
The sample comes from the next 150 finishers of a 10-kilometer race. These are people who not only chose to participate in a relatively long race but also were able to finish it. Think about whether this group is typical of all adults in the county, including those who do not run, are less active, or have health issues.
Decide whether the sample is representative or biased
People who run and finish a 10-kilometer race are very likely to exercise regularly, probably more than the average adult. Since the sample includes only these race participants, it overrepresents frequent exercisers and underrepresents less active adults. This means the sampling method introduces bias: the sample systematically differs from the population in a way related to the question being studied.
Check other descriptions and choose the accurate one
The survey results cannot be claimed to describe all adults in the county (so any statement generalizing to the whole population is not justified), increasing the number of race finishers would not fix the underlying bias, and this is not an experiment because no treatment is imposed—participants are only being asked questions. Therefore, the accurate description is: The sample is biased because it includes only people who participate in the race.