Question bank / Inference from sample statistics and margin of error

Math · Problem-Solving and Data AnalysisHard

Two polls each surveyed a different random sample of 500500 adults from the same population about whether they plan to buy an electric vehicle. Poll 1 found that 34%34\% plan to buy one, with a margin of error of 4.24.2 percentage points. Poll 2 found 39%39\%, with a margin of error of 4.34.3 percentage points. Which of the following is a plausible value for the population percentage that is consistent with both polls?

A

30%30\%

B

36%36\%

C

42%42\%

D

44%44\%

Show answer and explanation

Answer: B

Poll 1 gives a plausible interval of 34±4.234 \pm 4.2, or 29.8%29.8\% to 38.2%38.2\%. Poll 2 gives 39±4.339 \pm 4.3, or 34.7%34.7\% to 43.3%43.3\%. A value consistent with both must lie in the overlap, 34.7%34.7\% to 38.2%38.2\%. Only 36%36\% is in that overlap.

Choice A is plausible for poll 1 but falls below poll 2's interval, which starts at 34.7%34.7\%.

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