{a} Consider testing the hypotheses Hg versus H1 at the 0.135 level of signicance using one ohseivation .v (n = 1). (1') Determine the critical value, c' of the test that rejects Ha if Iv 1.11.3.3 _" c. 1|What is the power of the test at 5' = 3'? {4+4} (ii) Determine the critical value, c, of the test that rejects H1) if Iv 111.1? 2... c. What is the power of the test at E? = 3'? {4+4} (iii) Which of the the tests in parts (i) and (ii) is more preferable and why-\"3r (4) Let X1, X2, X3, ..., Xn be a random sample from a distribution whose probability density function is either: 1 if0 1, Ho : f (x) = or H1 : f (x) = 0 otherwise otherwise Given: The cumulative distribution function of Y = - In X under Ho is 0 ify