Let X1, . . . , Xn iid N (, 1) ( R). Test H0 : 0 against H1 : > 0 based on T (X1, . . . , Xn) = d d log p(X1, . . . , Xn) =0 s E d2 d 2 log p(X1, . . . , Xn) =0 , where both the loglikelihood function in the numerator and the Fisher information in the denominator are evaluated at = 0. (a) Work out T (X1, . . . , Xn) and simplify as much as possible. (b) Obtain the distribution of T (X1, . . . , Xn) under H0 : 0 using the Central Limit Theorem. 4