To compare two variances in the normal case, let 1, 2,, n be i.i.d. (independently and identically distributed) (x, x 2) and let 1, 2,, n be i.i.d. (&, )where the

X's and the Y's are independent samples. Argue that under 0: x^2 = y^2

!

&

! ~$(#,'(#

where %

! (respectively, &

!) denotes the sample variance for the X (respectively, the Y)

sample.

Construct a confidence interval for the ratio *! "

*#

".