SAT Inference from sample statistics and margin of error Practice Question 1 (Medium) | SAT Owl

Question bank / Inference from sample statistics and margin of error

Math · Problem-Solving and Data AnalysisMedium

A polling company selected a random sample of $400$ registered voters in a county and found that $62\%$ of them support a proposed library tax. The margin of error for the estimate is $4$ percentage points. Which of the following is the most appropriate conclusion?

A

Exactly $62\%$ of all registered voters in the county support the tax.

B

Between $58\%$ and $66\%$ of the voters in the sample support the tax.

C

Between $60\%$ and $64\%$ of all registered voters in the county support the tax.

D

It is plausible that between $58\%$ and $66\%$ of all registered voters in the county support the tax.

Show answer and explanation

Answer: D

A margin of error describes uncertainty about the population, not the sample. Adding and subtracting $4$ percentage points from $62\%$ gives a plausible range of $58\%$ to $66\%$ for all registered voters in the county. The word "plausible" matters, because the true value is not guaranteed to fall in the interval.

Choice B has the right interval but applies it to the sample, whose percentage is known exactly to be $62\%$ .

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