A researcher wants to estimate the prevalence of hypertension in a district. Expected prevalence is 30%, acceptable error is 5% (absolute), and 95% confidence level. The minimum sample size required using the formula n = Z²pq/d² is:

• A 246
• B 323
• C 423
• D 323 ✓

Explanation

n = Z²pq/d² where Z = 1.96 (for 95% CI), p = 0.30, q = 0.70, d = 0.05. n = (1.96)² × 0.30 × 0.70 / (0.05)² = 3.8416 × 0.21 / 0.0025 = 0.8067 / 0.0025 = 322.7 ≈ 323. This is the standard cross-sectional sample size formula for estimating proportion. Increasing confidence level to 99% (Z = 2.58) or reducing allowable error would increase the required n. Adding a design effect (DEFF) for cluster sampling would multiply n by the DEFF.

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

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