Comparing Two Population Variances For use with

Chapter 9, Problem 9.7.9

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Comparing Two Population Variances For use with 9.7.109.7.12. Recall that if S2 x is the sample variance of a set of n observations from a normal distribution with variance 2 A, then S2 x 2 A 2 n1 n1 and that if S2 y is the sample variance of a set of m observations from a normal distribution with variance 2 B, thenS2 y 2 B2 m1 m1 (a) Explain why 2 AS2 y 2 BS2 x Fm1,n1(b) Show that part (a) implies that PF1/2,m1,n1 2 AS2 y 2 BS2 x F/2,m1,n1 =1 or alternatively that P 1 F/2,n1,m1 2 AS2 y 2 BS2 x F/2,m1,n1 =1 (c) Deduce that2 A 2 B s2 x s2 y F/2,n1,m1,s2 x F/2,m1,n1 s2 y is a 1 level two-sided condence interval for the ratio of the population variances.If such a condence interval contains the value 1, then this indicates that it is plausible that the population variances are equal. An unfortunate aspect of these condence intervals, however, is that they depend heavily on the data being normally distributed, and they should be used only when that is a fair assumption. You may be able to obtain these condence intervals on your computer package.