(a)Supposethat has a normal distribution with mean and variance 2=36. Let the rejection region be defined by ={:0.(i)Find the uniformly most powerful test of size =0.03for testing the null hypothesis 0:=0.35against the alternative hypothesis 1:

(a) Suppose that X has a normal distribution with mean a and variance o = 36. Let the rejection region be defined by RR = {X: X 0. (i) Find the uniformly most powerful test of size a = 0.03 for testing the null hypothesis Ho: u = 0.35 against the alternative hypothesis H1: u