Problem-Solving and Data AnalysisHardSample size needed to halve a margin of error
Problem-Solving and Data Analysis practice question
A survey of 400 randomly chosen people has a certain margin of error. About how many people should a new survey include to halve that margin of error?
Answer: 1600
The margin of error shrinks with the square root of the sample size, so halving it needs four times as many people: 1,600.
Common wrong answers
- If you answered 200
- 200 halves the sample and enlarges the margin.
- If you answered 800
- 800 doubles the sample, which reduces the margin by a factor of about 1.4, not 2.
- If you answered 3200
- 3200 multiplies by 8.
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