From two normal populations with respective variances 2 1 and 2 2 , we observe

Chapter 10, Problem 10.81

(choose chapter or problem)

From two normal populations with respective variances 2 1 and 2 2 , we observe independent sample variances S2 1 and S2 2 , with corresponding degrees of freedom1 = n11 and 2 = n21. We wish to test H0 : 2 1 = 2 2 versus Ha : 2 1 = 2 2 . a Show that the rejection region given by F > F1 2,/2 or F < F2 1,/2 1 , where F = S2 1 /S2 2 , is the same as the rejection region given by S2 1 /S2 2 > F1 2,/2 or S2 2 /S2 1 > F2 1,/2 . b Let S2 L denote the larger of S2 1 and S2 2 and let S2 S denote the smaller of S2 1 and S2 2 . Let L and S denote the degrees of freedom associated with S2 L and S2 S , respectively. Use part (a) to show that, under H0, P S2 L /S2 S > FL S ,/2 = . Notice that this gives an equivalent method for testing the equality of two variances.