23. Let (ZI ' . '. ' ZN) "" (XI' .. . ' Xm , Y1, · · · , Yn ) be distributed according to the joint density (56) of Chapter 5, and consider the problem of testing H: 71 "" against the alternatives that the X's and Y's are independently normally distributed with common variance 0 2 and means 71 '" Then the permutation test with rejection region IY - XI > crT( Z»), the two-sided version of the test (55) of Chapter 5, is most stringent. [Apply Problem 22 with each of the sets 0t. consisting of two points (~I 711, 0), a2' 71 2, 0) such that _n_ 8, ~I = r - m + n n €2 "" r + --8, m + n for some r and 8.) m 711 =r+ --8; m+n 712 = r - ~8