7. Consider the Z-test that rejects Ho if Zn > Za, where za is the (1 - a) quantile of N(0, 1). Suppose that | |2/V2n -+ 0 as n - co. Show that this test, which we call x'-Z-test in the sequel, has asymptotic power &(0 - za), where & is the CDF of N(0, 1). (It suffices to prove the result assuming the approximate distribution from the last problem as the true distribution. The result implies that, asymptotically, if |lull?/ Vn -> co, then the x2-Z-test has full power; if |lull?/vn - 0, then the test is powerless.)