SAT Math · Inference from sample statistics and margin of error · medium
Survey A estimates that 52% of a population supports a proposal, with a margin of error of 4 percentage points. Survey B estimates that…
Survey A estimates that 52% of a population supports a proposal, with a margin of error of 4 percentage points. Survey B estimates that 48% supports the same proposal, with a margin of error of 5 percentage points. Based on this information, which conclusion is best supported?
Answer and explanation
Answer: B: The two surveys do not provide clear evidence that the true level of support differs, since their margin-of-error intervals overlap.
Convert each estimate to an interval. Survey A gives , which is 48% to 56%. Survey B gives , which is 43% to 53%. The intervals overlap from 48% to 53%, so some values of true support are plausible under both surveys, and the data do not clearly show a difference. That supports choice B. Choice A overstates the evidence, since a survey cannot prove anything about the true value. Choice C is wrong because overlapping intervals are consistent, not contradictory. Choice D fails because the interval for A includes values below 50%, so support above 50% is not certain.
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