A random sample of 600 voters in a district was asked whether... | SAT Inference from sample statistics and margin of error Question, Answer Explained

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Math · Problem-Solving and Data AnalysisMedium

A random sample of $600$ voters in a district was asked whether they support a proposed park. Based on the sample, the plausible values for the percent of all voters in the district who support the park are from $41\%$ to $49\%$ . How many of the $600$ sampled voters said they support the park?

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Answer: 270

The sample percent is the center of the interval, $\frac{41 + 49}{2} = 45\%$ , and the margin of error is $4$ percentage points. So $0.45 \times 600 = 270$ of the sampled voters support the park.

Using an endpoint, $41\%$ or $49\%$ , gives $246$ or $294$ , but the sample percent is the midpoint of the interval.

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