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

A normal population has known standard deviation 12. A 95% confidence interval for the mean is to have total width at most 6. Using z = 1.96, what is the smallest sample size required?

The smallest sample size is 62. Requiring 2 times 1.96 times 12 over root n to be at most 6 gives root n at least 7.84, so n at least 61.47, which must be rounded up to 62.

  1. A62Correct
  2. B16
  3. C246
  4. D31
  5. 61

Explanation

Width = 2 x 1.96 x 12/sqrt(n) ≤ 6, so sqrt(n) ≥ 47.04/6 = 7.84. Then n ≥ 61.47, so n = 62. Using 61 rounds down, which fails the width requirement; 246 uses total width as half-width incorrectly.

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