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?
- A. Survey 2's estimate is likely to be closer to the true proportion because its sample is larger.Correct
- B. Survey 1's estimate is likely to be closer because a smaller sample is easier to manage.
- C. Both estimates are equally reliable because both samples are random.
- 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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