SAT Inference from sample statistics and margin of error Practice Question 6 (Medium) | SAT Owl

Question bank / Inference from sample statistics and margin of error

Math · Problem-Solving and Data AnalysisMedium

A park has $900$ trees. A biologist examined a random sample of $60$ of the trees and found that $15\%$ had a certain leaf disease. The margin of error for this estimate is $9$ percentage points. Is it plausible that more than $20\%$ of the trees in the park have the disease?

A

No, because the sample proportion is $15\%$ , which is less than $20\%$ .

B

Yes, because the plausible values for the population proportion range from $6\%$ to $24\%$ , which includes values greater than $20\%$ .

C

No, because $20\%$ is greater than the margin of error of $9\%$ .

D

Yes, because $9$ of the $60$ trees in the sample had the disease.

Show answer and explanation

Answer: B

The margin of error gives an interval of plausible values for the population proportion: $15\% \pm 9\%$ , or $6\%$ to $24\%$ . Values between $20\%$ and $24\%$ are in this interval, so it is plausible that more than $20\%$ of the park's trees have the disease.

Choice A treats the sample proportion as the exact population proportion, ignoring the margin of error.

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