A study of fasting blood glucose in 100 subjects yields a standard deviation of 20 mg/dL. If the study were repeated on 400 subjects drawn from the same population, the standard error of the mean would be:

• A Unchanged at 2 mg/dL
• B Reduced to 0.5 mg/dL
• C Increased to 4 mg/dL
• D Reduced to 1 mg/dL ✓

Explanation

Standard error of the mean equals SD divided by the square root of n. With n = 100, SE = 20/10 = 2 mg/dL. Quadrupling the sample size doubles the square root of n, so the new SE = 20/20 = 1 mg/dL. This illustrates that precision improves with the square root of sample size, meaning large increases in n yield progressively smaller gains in precision.

Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.

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