SAT Math · Inference from sample statistics and margin of error · hard
Survey A samples 2,000 people and reports a margin of error of 2 percentage points. Survey B samples 500 people and reports a margin of…
Survey A samples 2,000 people and reports a margin of error of 2 percentage points. Survey B samples 500 people and reports a margin of error of 4 percentage points, on the same underlying question. Which statement is best supported by this information?
Answer and explanation
Answer: B: Survey A's larger sample size is consistent with its smaller margin of error, since larger samples generally produce more precise estimates.
Larger samples generally produce more precise estimates and therefore smaller margins of error. Survey A has 2,000 respondents and a margin of 2 points, while Survey B has 500 respondents and a margin of 4 points, which fits that pattern. That makes B correct. Choice A is backward: a larger margin of error means less precision. Choice C is false because the margins differ. Choice D overreaches, because the margin of error describes typical sampling variation, not a guarantee that any one result is closer to the truth; Survey B's estimate could happen to be nearer.
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