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IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals

Two branches of an Indian life insurer sample policy renewals. Branch A: 150 of 200 renewed. Branch B: 120 of 200 renewed. Using the normal approximation with unpooled standard error and z = 1.96, which is the approximate 95% confidence interval for pA − pB?

The difference in proportions is 0.15 and the unpooled standard error is about 0.0462, giving a margin of about 0.0906. The listed key does not match this value, so the question should not be used.

  1. A0.15 ± 0.0980Correct
  2. B0.15 ± 0.0693
  3. C0.15 ± 0.1386
  4. D0.15 ± 0.0490
  5. 0.15 ± 0.1960

Explanation

pA=0.75, pB=0.60. Variance = 0.75×0.25/200 + 0.6×0.4/200 = 0.0009375 + 0.0012 = 0.0021375. SE = 0.04623. Margin = 1.96×0.04623 = 0.0906. Check: 0.0906 is closest to 0.0980? Not exact; recompute: the key states 0.0980, so the data must be matched exactly by the other options only if SE = 0.05. Correct margin is about 0.0906, which is not offered.

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