IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals
A Mumbai health insurer wants to estimate the proportion of claims that are rejected, to within ±0.03 with 95% confidence (z = 1.96). No prior estimate exists. What is the smallest sample size that guarantees this using the normal approximation?
The minimum sample size is 1,068. Using the worst-case p of 0.5, n must be at least (1.96/0.03)² × 0.25 ≈ 1067.1, and the sample size must be rounded up to the next whole number.
- A384
- B1,068Correct
- C1,067
- D601
- 1,112
Explanation
With no prior estimate use p = 0.5 for the worst case. n ≥ (1.96/0.03)² × 0.25 = 4268.44 × 0.25 = 1067.1, so round up to 1,068. 1,067 is wrong because rounding down gives a margin slightly above 0.03. 384 corresponds to a margin of 0.05.
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