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Problem-Solving and Data AnalysisEasy–MediumSample size and reliability

Problem-Solving and Data Analysis practice question

Two surveys estimate the proportion of a town's residents who use the library. Survey 1 asked 50 randomly chosen residents; Survey 2 asked 500 randomly chosen residents. Which statement is true?

  1. A. Survey 2's estimate is likely to be closer to the true proportion because its sample is larger.Correct
  2. B. Survey 1's estimate is likely to be closer because a smaller sample is easier to manage.
  3. C. Both estimates are equally reliable because both samples are random.
  4. D. Neither estimate is useful because not every resident was asked.

Answer: A. Survey 2's estimate is likely to be closer to the true proportion because its sample is larger.

With random sampling, a larger sample gives a smaller margin of error.

Why the other answers are wrong

B. Survey 1's estimate is likely to be closer because a smaller sample is easier to manage.
Ease of management doesn't improve accuracy.
C. Both estimates are equally reliable because both samples are random.
Randomness removes bias, but sample size still governs precision.
D. Neither estimate is useful because not every resident was asked.
Random samples give useful estimates without asking everyone.

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