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IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit

Independent normal samples have sizes 11 and 16 with sample variances 30 and 12. To test H0: sigma1^2 = sigma2^2 against H1: sigma1^2 > sigma2^2, the F statistic is formed with the larger variance in the numerator. Which option gives the correct statistic and degrees of freedom?

The statistic is 2.5 on (10, 15) degrees of freedom. It is the ratio of the sample variances, 30 over 12, with numerator degrees of freedom 11 minus 1 and denominator degrees of freedom 16 minus 1.

  1. AF = 2.5 on (15, 10) degrees of freedom
  2. BF = 2.5 on (10, 15) degrees of freedomCorrect
  3. CF = 0.4 on (10, 15) degrees of freedom
  4. DF = 2.5 on (11, 16) degrees of freedom
  5. F = 2.73 on (10, 15) degrees of freedom

Explanation

F = s1^2/s2^2 = 30/12 = 2.5. Degrees of freedom are numerator n1-1 = 10 and denominator n2-1 = 15. Swapping them gives option A, using n gives D, and inverting the ratio gives 0.4.

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