A study reports a standard deviation of 10 for hemoglobin levels with a sample size of 100 subjects. If the same study were repeated with 400 subjects but the same standard deviation, the standard error of the mean would change from its original value by a factor of:
- A Doubled (SE increases by 2×)
- B Quartered (SE decreases by 4×)
- C Halved (SE decreases by 2×) ✓
- D Remains unchanged regardless of sample size
Correct answer: C. Halved (SE decreases by 2×)
Explanation
Standard Error (SE) = SD/√n. With n=100: SE = 10/√100 = 10/10 = 1.0. With n=400: SE = 10/√400 = 10/20 = 0.5. The SE halves when sample size quadruples (since √400/√100 = 2). This reflects the fundamental principle that precision of estimation increases with larger samples, but the relationship is with the square root of n, not n itself.
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
High-yield for: NEET PGINI-CETNExTFMGEUSMLEPLABMRCP
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