In a survey of 1000 adults, 400 have hypertension. The 95% confidence interval for the prevalence is 36.96%–43.04%. If the sample size were increased to 4000 with the same observed prevalence (40%), the 95% CI would:
- A Widen because more data increases variability
- B Narrow because standard error is inversely proportional to √n ✓
- C Remain the same because prevalence has not changed
- D Shift to the right because the sample mean increases
Correct answer: B. Narrow because standard error is inversely proportional to √n
Explanation
The standard error of a proportion = √[p(1−p)/n]. As n increases four-fold (from 1000 to 4000), the standard error halves (√4 = 2), so the 95% CI narrows to approximately 38.5%–41.5%. The CI width reflects precision, not accuracy — a larger sample gives a more precise estimate of the true population proportion. The point estimate (prevalence) does not change with increased n if the observed proportion stays at 40%.
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
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