SAT Inference from sample statistics and margin of error Practice Question 7 (Hard) | SAT Owl

Question bank / Inference from sample statistics and margin of error

Math · Problem-Solving and Data AnalysisHard

A researcher surveyed a random sample of $500$ students at University A and found that $72\%$ of the sampled students live on campus. The margin of error for the estimate is $4$ percentage points. Which of the following is the most appropriate inference?

A

It is plausible that between $68\%$ and $76\%$ of all students at University A live on campus.

B

It is plausible that between $68\%$ and $76\%$ of all university students in the country live on campus.

C

Exactly $72\%$ of all students at University A live on campus.

D

Between $68\%$ and $76\%$ of the $500$ students surveyed live on campus.

Show answer and explanation

Answer: A

The sample was drawn at random from University A, so it supports inferences about University A's students only. The interval $72\% \pm 4\%$ gives plausible values from $68\%$ to $76\%$ for the population proportion. The proportion in the sample itself is known exactly: $72\%$ .

Choice B uses the correct interval but extends it to a population (all university students) that was not sampled.

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