Problem-Solving and Data AnalysisVery hardThe population a sample estimate describes
Problem-Solving and Data Analysis practice question
A cycling magazine emailed a survey to 1,000 randomly selected subscribers, and all of them responded. The mean time subscribers reported exercising was 6.2 hours per week, with a margin of error of 0.4 hours.
Which conclusion is best supported by these results?
- A. It is plausible that the mean weekly exercise time of all subscribers to the magazine is between 5.8 and 6.6 hours.Correct
- B. It is plausible that the mean weekly exercise time of all adults in the country is between 5.8 and 6.6 hours.
- C. Every subscriber to the magazine exercises between 5.8 and 6.6 hours per week.
- D. Reading the magazine causes subscribers to exercise about 6.2 hours per week.
Answer: A. It is plausible that the mean weekly exercise time of all subscribers to the magazine is between 5.8 and 6.6 hours.
A random sample supports conclusions about the population it was drawn from — here, subscribers to the magazine. The interval 6.2 plus or minus 0.4 gives 5.8 to 6.6 hours for that population's mean.
Why the other answers are wrong
- B. It is plausible that the mean weekly exercise time of all adults in the country is between 5.8 and 6.6 hours.
- The 1,000 people were selected at random from SUBSCRIBERS, not from adults in general. Subscribers to a cycling magazine are unlikely to be typical of everyone, so the estimate can't be stretched to the whole country.
- C. Every subscriber to the magazine exercises between 5.8 and 6.6 hours per week.
- The interval is about the population's mean, not about individuals. Some subscribers will exercise far more or far less while the average still lies in 5.8 to 6.6.
- D. Reading the magazine causes subscribers to exercise about 6.2 hours per week.
- This is an observational survey with no comparison group and no assignment, so it can show what subscribers report — not that the magazine caused it. People who already cycle a lot are the ones likely to subscribe.
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