SAT Inference from sample statistics and margin of error Practice Question 12 (Medium) | SAT Owl

Question bank / Inference from sample statistics and margin of error

Math · Problem-Solving and Data AnalysisMedium

A random sample of $1{,}000$ adults in a country found that $41\%$ exercise daily. The margin of error for this estimate is $3$ percentage points. A news report claims that fewer than half of the adults in the country exercise daily. Is the claim supported by the survey?

A

Yes, because all plausible values for the population percentage, $38\%$ to $44\%$ , are less than $50\%$ .

B

No, because the sample included only $1{,}000$ adults.

C

No, because $41\%$ is within $10$ percentage points of $50\%$ .

D

Yes, because exactly $41\%$ of the adults in the country exercise daily.

Show answer and explanation

Answer: A

The margin of error gives a plausible range of $41\% \pm 3\%$ , or $38\%$ to $44\%$ , for all adults in the country. Every value in that range is below $50\%$ , so the survey supports the claim that fewer than half exercise daily.

Choice D reaches the right answer for the wrong reason; the population percentage is not known to be exactly $41\%$ .

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free.