A public health researcher wants to estimate the prevalence of anaemia in rural India with a 95% confidence level and an acceptable error of 5%. The assumed prevalence is 40%. Using the standard formula n = Z²pq/d², the minimum sample size required is approximately:

• A 138
• B 246
• C 196
• D 369 ✓

Explanation

Using n = Z²pq/d²: Z for 95% CI = 1.96, p = 0.40, q = 0.60, d = 0.05. n = (1.96)² × 0.40 × 0.60 / (0.05)² = 3.8416 × 0.24 / 0.0025 = 0.9220 / 0.0025 = 368.6, rounded to approximately 369. This formula is for simple random sampling; cluster or stratified designs require a design effect multiplier. When expected prevalence is unknown, 50% is assumed (gives the maximum n of 384 at 5% error, 95% CI). The sample size increases as d decreases or as confidence level increases.

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

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