Problem-Solving and Data AnalysisVery hardSample size needed to halve a margin of error
Problem-Solving and Data Analysis practice question
A researcher's random sample gives an estimate with a certain margin of error. Keeping the confidence level the same, the researcher wants a margin of error HALF as large. By what factor must the sample size be multiplied?
Answer: 4
The margin of error shrinks in proportion to the square root of the sample size. To cut it in half, the square root must double, so the sample size must be multiplied by 2² = 4.
Common wrong answers
- If you answered 2
- Doubling the sample size shrinks the margin by a factor of √2 (about 1.4), not 2.
- If you answered 8
- 8 would shrink the margin by a factor of √8 ≈ 2.8, more than required; 4 is enough.
- If you answered 0.5
- Halving the sample size would make the margin LARGER, not smaller.
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