Problem-Solving and Data AnalysisVery hardSample size for a smaller margin of error
Problem-Solving and Data Analysis practice question
A survey of 625 randomly chosen residents gives an estimate with a margin of error of 4 percentage points. Approximately how many residents would need to be surveyed to reduce the margin of error to 2 percentage points?
Answer: 2500
Halving the margin of error requires four times the sample size: 4 × 625 = 2,500.
Common wrong answers
- If you answered 313
- 313 halves the sample, which would enlarge the margin.
- If you answered 1250
- 1250 doubles the sample, which reduces the margin only by a factor of √2.
- If you answered 10000
- 10000 multiplies by 16, reducing the margin to 1 point.
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