SAT OwlQuestion bank / Inference from sample statistics and margin of error
A researcher selected a random sample of adults in a large city and asked whether they had used the city's bike-share program in the past month. The estimate for all adults in the city had a margin of error of percentage points. Of the sampled adults, were ages to , and the researcher used their responses to estimate the percent of all city adults ages to who had used the program. Which of the following is most likely true about the margin of error for this second estimate?
It is greater than percentage points, because the estimate is based on a smaller sample.
It is less than percentage points, because adults ages to are more similar to one another.
It is equal to percentage points, because both estimates come from the same survey.
It is less than percentage points, because the subgroup is part of the full sample.
Show answer and explanation
Answer: A
The margin of error depends on the size of the sample used for the estimate. The estimate for adults ages to uses only of the responses. A smaller sample has more sampling variability, so the margin of error is expected to be greater than percentage points.
Choice C is tempting because the data come from one survey, but the second estimate relies on only people instead of .
Why the other choices are wrong
- B. The margin of error depends mainly on how many responses an estimate uses, and this estimate uses fewer.
- C. The second estimate uses only 250 of the 1,000 responses, so it has more sampling variability.
- D. Being part of the full sample doesn't help. The subgroup estimate still rests on only 250 responses.
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