A4. (i) What is meant by a Neyman-Pearson (Likelihood Ratio) test of a simple null hypothesis H. :0 =0, against a simple alternative hypothesis H, :0 = 0, where O is a real parameter? (5 Marks) (ii) Let I denote a typical Neyman-Pearson test of the above hypotheses stated in (i) above and K. (0) the power function of this test. Prove that Ky. ( 0, ) 2 Ky. ( 0). (5 Marks) A5. A colleague has used statistical methods in the analysis of data but has been told that he is using a frequentist approach whereas a Bayesian method might be better. He asks you to describe how the approaches differ, and how easy the Bayesian approach is to use. What would be your reply? (5 Marks) A6. State the asymptotic property of the generalized likelihood ratio test (GLRT) in testing a given hypothesis and its corresponding critical region of size a . (4 marks)