A researcher draws two independent random samples from the same population to estimate mean hemoglobin. Sample A has n=100, Sample B has n=400. The ratio of the width of the 95% confidence interval for Sample A to that for Sample B is:
- A 1:1
- B 1:2
- C 2:1 ✓
- D 4:1
Correct answer: C. 2:1
Explanation
Confidence interval width is proportional to 1/sqrt(n). Sample A has n=100, Sample B has n=400. The ratio of widths is sqrt(400)/sqrt(100) = 20/10 = 2:1, meaning Sample A's interval is twice as wide. Option B inverts the ratio. Option D confuses n with sqrt(n). Understanding how sample size affects precision is essential for study planning questions.
Reference: Methods in Biostatistics, 7th ed.
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