28) Single mistake one downvote

Let (Xi1, ..., Xin), i = 1, 2, be two independent random samples from N(i, 2 i ), respectively, where n > 1 and is and is are unknown. Show that a UMPU test of size for testing H0 : 2 2 = 02 1 versus H1 : 2 2 = 02 1 rejects H0 when max S2 2 0S2 1 , 0S2 1 S2 2 > 1 c c , where 0 > 0 is a constant, c 0 f(n1)/2,(n1)/2(v)dv = /2 and fa,b is the Lebesgue density of the beta distribution with parameter (a, b).