(X1,..., Xn) be a random sample from Exercise 21 (#6.36). Let X = N(u, 02) with unknown u and o2. (i) Show that the power of the one-sample t-test depends on a noncentral t-distribution. (ii) Show that the power of the one-sample t-test is an increasing function of (u - Mo)/o for testing Ho: Mo versus H : H > Mo and of lu Mol/o for testing Ho : p = Mo versus H :p #Mo, where Ho is a known constant. Note. For testing Ho : u suo versus H1 :u > Ho, the one-sample t-test of size a rejects Ho if and only if t(X) > tn-1,a, where t(X) = n(-uo)/S, X is the sample mean, S2 is the sample variance, and tr,a is the (1 - a)th quantile of the t-distribution tr. For testing Ho : u = Ho versus H1 : 1 Mo, the one-sample t-test of size a rejects Ho if and only if |t(X)| > tn-1,0/2