A study measures serum vitamin D levels in 64 healthy adults and reports a standard deviation of 16 ng/mL. The researcher then repeats the study with a larger sample of 256 adults from the same population and obtains the same standard deviation. How does the standard error of the mean change?
- A It remains unchanged
- B It becomes one-fourth of the original
- C It becomes one-half of the original ✓
- D It doubles
Correct answer: C. It becomes one-half of the original
Explanation
Standard error of the mean equals the standard deviation divided by the square root of the sample size. When the sample size increases from 64 to 256, which is a fourfold increase, the square root of the sample size doubles from 8 to 16, so the standard error becomes half of its original value. Option B incorrectly assumes a linear relationship with sample size rather than with its square root.
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
High-yield for: NEET PGINI-CETNExTFMGEUSMLEPLABMRCP
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