5. Let Zl' . .. ' Z" be independently normally distributed with common variance 0 2 and means E(Z;) = ;(i = 1, . . . , s) , E(Z;) = 0 (i = s + 1, ... , n) . There exist UMP unbiased tests for testing ~l ~~? and ~l =~? given by the rejection regions Zl - ~:) n L Z//(n - s) ; - s+1 IZI - r?1 n L Zp/(n-s) ;-s+ 1 When ~I = ~:) the test statistic has the r-distribution with n - s degrees of freedom . *A system atic account of this distribution can be found in John son and Kotz (1970. Vol. 2. Chapter 31) and in Owen (1985)