SAT Math · Inference from sample statistics and margin of error · hard
A random sample of 1,000 adults found that 40% own a particular type of car, with a margin of error of 3 percentage points for the full…
A random sample of 1,000 adults found that 40% own a particular type of car, with a margin of error of 3 percentage points for the full sample. A researcher also reports an estimate specifically for the 150 sampled adults under age 30. Which statement about the margin of error for this under-30 subgroup is most accurate?
Answer and explanation
Answer: D: The subgroup's margin of error is likely larger than 3 percentage points, since it is based on a smaller number of respondents.
Margin of error depends on sample size: larger samples give smaller margins, and smaller samples give larger ones. The full sample has 1,000 respondents with a 3-point margin. The under-30 subgroup has only 150 respondents, so each estimate has less data behind it and a larger margin of error, choice D. Choice A assumes the margin is the same regardless of sample size. Choice B claims a narrower group gives a smaller margin, which reverses the relationship. Choice C is false because margins of error can be computed for subgroups. The key is the number of respondents in the group, not how specific the group is.
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