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Unformatted text preview: where 2 is the critical value for a 2 distribution with n-1 degrees of freedom. 3. Suppose that Y is a random sample of size 1 from a population with density f ( y | ) = ( y -1 , y 1 , elsewhere. where > 0. (a) Sketch the power function of the test with the critical region Y > . 5. (Compute the power at a reasonable number of points and draw a curve that seems to t those values. Please be neat.) (b) Find the best test for testing H : = 1 versus H A : = 2 of size . ( ? ) Show that you get the same test for any alternative where H A : = t and t > 1. 4. Show that if T is a sucient statistic for estimating from the data X 1 ,...,X n then the Generalized Likelihood Ratio Test (GLRT) statistic for testing H : versus H a : 6 is a function of T . (Hint: use the factorization theorem.) 1...
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- Spring '08