Problem-Solving and Data AnalysisVery hardSample size for a third of the margin
Problem-Solving and Data Analysis practice question
A random sample of 200 people gives an estimate with a certain margin of error. The margin of error shrinks in proportion to the square root of the sample size. Which sample size would give a margin of error closest to ONE-THIRD of that margin?
- A. 1,800Correct
- B. 600
- C. 66
- D. 5,400
Answer: A. 1,800
To divide the margin by 3, the square root of the sample size must triple, so the sample size must be multiplied by 3² = 9: 200 × 9 = 1,800.
Why the other answers are wrong
- B. 600
- 600 triples the sample, which divides the margin only by √3 ≈ 1.7.
- C. 66
- 66 is a third of the sample, which makes the margin LARGER.
- D. 5,400
- 5,400 multiplies by 27, dividing the margin by about 5.2 — more than asked.
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