SAT Inference from sample statistics and margin of error Practice Question 3 (Medium) | SAT Owl

Question bank / Inference from sample statistics and margin of error

Math · Problem-Solving and Data AnalysisMedium

Two researchers each selected a random sample of adults from the same city to estimate the proportion who commute by bicycle. Researcher A used a sample of $200$ adults, and the estimate had a margin of error of $6.9\%$ . Researcher B used a sample of $800$ adults and the same method. Which of the following is the most plausible margin of error for researcher B's estimate?

A

$3.5\%$

B

$6.9\%$

C

$9.8\%$

D

$13.8\%$

Show answer and explanation

Answer: A

When a sample is selected the same way from the same population, a larger sample size produces a smaller margin of error. Researcher B's sample is $4$ times as large, so the margin of error should be smaller than $6.9\%$ . The only choice less than $6.9\%$ is $3.5\%$ .

Choice D assumes a larger sample means a larger margin of error, but more data gives a more precise estimate.

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