A study reports a standard deviation of 12 for a sample of 36 observations. The standard error of the mean is 2. If the sample size were increased to 144 with the same standard deviation, the new standard error would be:
- A 0.5
- B 1.0 ✓
- C 3.0
- D 6.0
Correct answer: B. 1.0
Explanation
SEM = SD / sqrt(n). New SEM = 12 / sqrt(144) = 12 / 12 = 1.0. The sample size quadrupled from 36 to 144, so SEM is halved from 2 to 1. Option A would require n=144 with SD=6. Option C forgets the square root. Option D incorrectly multiplies. This tests understanding of the inverse square-root relationship between SEM and n.
Reference: Basic and Clinical Biostatistics, 4th ed.
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