Suppose that X1,X2, ...,Xn i.i.d N N(p,1). 1. We test hypothesis H0 : p. : 0 vs. H1 : p. : #1 (p1 % 0). Find the reject region at level 0: with a likelihood ratio approach. Calculate the typeI error and typeH error respectively. 2. Prove that when the null hypothesis above is true, pvalue follows uniform distribution U[0, I] . 3. Find an Ozlevel test for the problem H0 : p, = 0 vs. H1 : p > 0. Compute its power function. 4. Find an Ozlevel test for the problem H0 : p. = 0 vs. H1 : p. 7g 0. Compute its power function