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

Independent samples of sizes 8 and 6 are taken from two normal populations with equal variances. The sample variances are 12 and 4 respectively. What is the F statistic S1^2/S2^2 and its degrees of freedom?

The statistic is 12/4 = 3 and it follows an F distribution with 7 numerator and 5 denominator degrees of freedom, since the degrees of freedom are each sample size minus one.

  1. A3, with 7 and 5 degrees of freedomCorrect
  2. B3, with 8 and 6 degrees of freedom
  3. C3, with 5 and 7 degrees of freedom
  4. D1/3, with 7 and 5 degrees of freedom
  5. 2, with 7 and 5 degrees of freedom

Explanation

Under equal variances S1^2/S2^2 ~ F(n1-1, n2-1) = F(7,5). Ratio = 12/4 = 3. Swapping the degrees of freedom or using n instead of n-1 is wrong.

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