Problem-Solving and Data AnalysisMediumSample size and confidence
Problem-Solving and Data Analysis practice question
Two surveys estimate the proportion of a city's residents who cycle to work. Survey 1 asked 100 random residents and found 20%. Survey 2 asked 2,000 random residents and found 18%. Which statement is true?
- A. Survey 2's estimate is more precise because its sample is larger.Correct
- B. Survey 1's estimate is more precise because it found a higher percentage.
- C. The estimates are equally precise because both samples were random.
- D. Neither estimate is useful because they disagree.
Answer: A. Survey 2's estimate is more precise because its sample is larger.
A larger random sample gives a smaller margin of error.
Why the other answers are wrong
- B. Survey 1's estimate is more precise because it found a higher percentage.
- The size of the percentage has nothing to do with precision.
- C. The estimates are equally precise because both samples were random.
- Both are unbiased, but precision depends on sample size.
- D. Neither estimate is useful because they disagree.
- A 2-point difference is well within the smaller survey's margin.
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