31. For testing the hypothesis H': 81 s 8 s 82 (81 s 82 ) against the alternatives 8 < 81 or 8 > 82 , or the hypothesis 8 = 80 against the alternatives 8 oF 80 , in an exponential family or more generally in a family of distributions satisfying the assumptions of Problem 30, a UMP test does not exist. (This follows from a consideration of the UMP tests for the one-sided hypotheses HI: 8 81 and H2 : 8 .s 82 ,]