Problem-Solving and Data AnalysisHardSample size for a target margin
Problem-Solving and Data Analysis practice question
A pilot poll of 400 randomly selected people produced a margin of error of 4 percentage points. The margin of error shrinks in proportion to the square root of the sample size. How many people must the full poll sample, using the same method, to achieve a margin of error of 2 percentage points?
Answer: 1600
Halving the margin requires doubling the square root of the sample size, which means multiplying the sample size by 4: 400 × 4 = 1,600.
Common wrong answers
- If you answered 200
- 200 halves the sample, which makes the margin LARGER.
- If you answered 800
- 800 doubles the sample, which shrinks the margin only by √2 (to about 2.8 points).
- If you answered 3200
- 3,200 multiplies by 8, more than needed; the margin would be about 1.4 points.
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