Question: Let X1, . . . , Xn be independent U (0, ) random variables. To test H0 : 10 versus H1 : > 10, a

Let X1, . . . , Xn be independent U (0, ) random variables. To test H0 : 10 versus H1 : > 10, a researcher wants to use the test 1[X(n) > 9.5], which rejects the null hypothesis for values of X(n) greater than 9.5.

(1) Find the power function of this test.

(2) Find the size of this test.

(3) What sample size is required for this test to have power greater than or equal to .99 at 10.1?

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