10. Consider a random sample from some distribution that depends on the parameter 0 > 0. The hypotheses of interest are Ho: 0 <00 vs H₁: 0>00 for 00 = 2. We will consiser the test with rejection region R = {T < c}, where T = T(X) is the appropriate test statistic. The test statistic T is known to have the following PDF: Ө fo(t) = to+1' t> 1. (a) Find the power function for this test (as a function of 0 and c). (b) Find the value of c such that this test will be size a for 80 = 2. (c) Find the probability of a Type II error at 0 = 4. (d) If = 1, what is the probability of making an error? Is it Type I or Type II? (e) Assuming a = 0.10, what is the decision if the observed data provides t = 1.2?

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