5. Before an election, combining the results of 12,625 polls with 14,491,635 samples in total, it shows that 6,413,959 responders (44.3%) say they will vote for the rst candidate and 6,134,272 responders (42.3%) say they will vote for the other candidate. Assume a binomial model Binomial (n, p) of the polls for the rst and second candidates, where p is the percentage of the votes to the rst candidate and n is the total number of votes to the rst candidate or the second candidate. Suppose we are interested in whether the rst candidate wins more than half of the votes to the rst and second candidates: H0: p=0.5v.s. H1: p>0.5 (a) Compute the test statistics of the generalized likelihood ratio test. Is this test a uniformly most powerful test? (b) Use Wilks' theorem to compute the critical value of the generalized likelihood ratio test under or = 0.05 level. Make a decision. (c) Another test has test statistics , where 190 = 0.5. Compute the pvalue of this test using the central limit theorem and make a decision. Assume the signicance level a: = 0.05. (d) If the second candidate wins the election, comment on possible prob- lems in this statistical analysis