Problem 5. (16 points) We want to test Whether a healthy diet makes a difference in treating diabetes. A group of 50 patients have a healthier diet and have their regular treatment in a month. 32 patients have their blood glucose level and 18 patients do not show improvement. Let the status of each patient Xi = 1 or 0 indicate the patient has improved or no no improvement respectively. Assume X|p ~ Bernoullia), for 3': 1,2, ..., 50. We test: H0:p=1/2 vs Ha:p71/2 (1) (4 points) Derive the rejection region of the Generalized Likelihood Ratio test. (2) (4 points) Based on Normal approximation compute the p-value of the GLRT test. (3) (6 points) Assume a uniform prior for p: 7r(p)=1 for0