Question: 1. Let Xl ' Xn be a sample from N(t 0 2). The power of Student's r-test is an increasing function of ~/o in

1. Let Xl" ' " Xn be a sample from N(t 0 2). The power of Student's r-test is an increasing function of ~/o in the one-sided case H : s 0, K: > 0, and of I~II0 in the two-sided case H : = 0, K: ':F O. [If I 1 -2 S = - i..(X; - X) , n - 1 the power in the two-sided case is given by 1- p{_ CS _ In~ s In(¥-~) s cs _ In~} o 0 0 0 0 and the result follows from the fact that it holds conditionally for each fixed value of Slo.]

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