Question: 13.10.3 Assume that the hypothesis Ho : 6 = 0 is to be tested against H I : B > 0, where 6 is a

13.10.3 Assume that the hypothesis Ho : 6 = 0 is to be tested against H I : B > 0, where 6 is a parameter in the U[6,0 + 11 distribution. (i) Derive the test of size cr = 0.05, based on one observation only, and obtain its power function for 6 =

0.1,0.2, . . . ,0.9. (ii) Use Monte Carlo simulations to obtain a test with a critical region > k ; that is, estimate k. Then again use Monte Carlo simulations to estimate the power function of this test at 6 = 0.1,0.2, . . . ,0.9. Use the same size cr = 0.05. (iii) Compare the power functions of both tests.

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