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 X3- = 1 or 0 indicate the patient has improved or no no improvement respectively. Assume Xilp ~ Bernoullp), for 2': 1,2, ..., 50. We test: ngp=1/2 vs Hazpal/2 (1) (4 points) Derive the rejection region of the Generalized Likelihood Ratio test. (2) (4 points) Based on Normal approximation compute the pvalue of the GLRT test. (3) (6 points) Assume a uniform prior for p: 7r(p)=1 for O