Problem-Solving and Data AnalysisVery hardSample size needed to halve a margin of error
Problem-Solving and Data Analysis practice question
A researcher wants to halve the margin of error of a survey estimate while keeping the same method and confidence level. By what factor must the sample size be multiplied?
Answer: 4
The margin of error is proportional to 1/√n, so halving it requires 4 times the sample.
Common wrong answers
- If you answered 2
- 2 assumes the margin falls in proportion to the sample size.
- If you answered 8
- 8 is the factor for a margin one third the size, roughly, and does not follow from halving.
- If you answered 0.5
- 0.5 would shrink the sample.
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