Skip to content

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

For a 95% confidence interval for the ratio of two normal population variances sigma1^2/sigma2^2, based on s1^2 = 20 (n1 = 9) and s2^2 = 10 (n2 = 13), the F(8,12) upper 2.5% point is 3.51 and F(12,8) upper 2.5% point is 4.20. Which is the interval?

The sample variance ratio is 2. The lower limit divides by the F(8,12) point 3.51, giving 0.57. The upper limit multiplies by the F(12,8) point 4.20, giving 8.40. The interval is (0.57, 8.40).

  1. A(0.57, 7.02)
  2. B(0.48, 7.02)Correct
  3. C(0.57, 8.40)
  4. D(0.48, 8.40)
  5. (0.24, 4.20)

Explanation

Ratio of sample variances = 2. Lower = 2 / F(8,12)_0.975 upper = 2/3.51 = 0.570. Upper = 2 x F(12,8) upper = 2 x 4.20 = 8.40. So the interval is (0.57, 8.40), which is option C, not B.

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