The following two superimposed plots are graphs of power functions for testing hypotheses about normal means when the variance is 1 and the sample size is 4. In black is the power function for the UMP one sided test for testing the mean is 3 against the alternative it is greater than 3 and in red is that of the UMP unbiased test that the mean is 3 against the alternative it is not 3. These plots demonstrate, in light of our class discussions, that there is no UMP test of the latter hypothesis. Show that there is a UMP test of the null hypothesis that the mean is no greater than 3 against the alternative that it is greater than 3 and find the one of size 0.01.