Question: i.i.d. 3. Suppose you Will observe X1, . . . ,Xn ~ Expo(6) and plan to test Ho : 6 = 60 vs. H1 :

i.i.d. 3. Suppose you Will observe X1, . . . ,Xn ~ Expo(6) and plan to test Ho : 6 = 60 vs. H1 : 6 = 61. a) Write out the likelihood ratio statistic and explain Why the likelihood ratio test rejects for large values of X if 61 60. b) The sampling distribution for X for a given value 6 is Gamma(n, n6). Suppose n = 101 60 = 1 and 61 = 5. Use qgamma to nd an oz 2 0.05 rejection region Au for the test statistic X. c) Explain Why your rejection region AG in part b is also the rejection region for a uniformly most powerful (UMP) 1-sided test of level 01 = 0.05. State the hypotheses for this test

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