Skip to content

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

In a sample of 400 policyholders of a Pune-based insurer, 80 lapsed their policy within a year. Using the normal approximation, what is the approximate 95% confidence interval for the true lapse proportion? (Use z = 1.96.)

The interval is 0.200 ± 0.0392. The sample proportion is 0.2, the standard error is the square root of 0.2×0.8/400, which is 0.02, and multiplying by 1.96 gives a margin of 0.0392.

  1. A0.200 ± 0.0196
  2. B0.200 ± 0.0392Correct
  3. C0.200 ± 0.0784
  4. D0.200 ± 0.0020
  5. 0.200 ± 0.1568

Explanation

p̂ = 80/400 = 0.2. SE = sqrt(0.2×0.8/400) = sqrt(0.0004) = 0.02. Margin = 1.96×0.02 = 0.0392. The option 0.0196 uses z×SE/2 by mistake, and 0.0784 doubles the margin.

Did you get it right without looking?

One question tells you little. A timed set on Confidence intervals and prediction intervals shows your real accuracy, how long you take and where you lose marks.

Practise Confidence intervals and prediction intervalsFree diagnostic mock

More Confidence intervals and prediction intervals questions