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

A 95% confidence interval for a proportion based on a sample of size n is (0.30, 0.40). The same sample proportion is used, but the sample size is quadrupled to 4n. Assuming the normal approximation, what is the approximate new 95% interval?

The new interval is (0.325, 0.375). The original midpoint is 0.35 with half-width 0.05, and quadrupling the sample size halves the standard error, so the half-width falls to 0.025.

  1. A(0.30, 0.40)
  2. B(0.325, 0.375)Correct
  3. C(0.35, 0.37)
  4. D(0.3125, 0.3875)
  5. (0.25, 0.45)

Explanation

The midpoint is 0.35 and the half-width is 0.05. Quadrupling n halves the standard error, so the half-width becomes 0.025. The interval is (0.325, 0.375). The option (0.3125, 0.3875) wrongly divides the half-width by 4 only partially, and (0.25, 0.45) doubles it.

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