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IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions

A population of N = 1,000 claims has variance sigma squared = 360 (defined with divisor N). A simple random sample of n = 40 is taken without replacement. Using the finite population correction factor (N-n)/(N-1) applied to sigma squared/n, what is the variance of the sample mean, to 3 decimal places?

The variance is 8.649. Divide 360 by 40 to get 9, then multiply by the finite population correction 960/999 = 0.96096, giving about 8.649. Ignoring the correction gives 9, and using N instead of N-1 gives 8.640.

  1. A9.000
  2. B8.649Correct
  3. C8.640
  4. D9.375
  5. 8.100

Explanation

sigma squared/n = 360/40 = 9. Correction factor = 960/999 = 0.96096. Variance = 9 x 0.96096 = 8.6486, i.e. 8.649. Option 9.000 ignores the correction; 8.640 uses 960/1000 instead of 960/999.

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