Question: statistics. ump tests P4 Let X1, ..., X, be a random sample from the Poisson distribution P(A). (a) Find a UMP level-a test for testing

statistics. ump tests

P4 Let X1, ..., X, be a random sample from the Poisson distribution P(A). (a) Find a UMP level-a test for testing Ho: d do VS. H, : > > do. (b) Plot the power function of the test from part (a) when a = 0.05, A, = 2, and n = 10, and compare it to the power function for the same a and Xo, but when n = 25. What do you observe? Does it surprise you that the power function is monotone in A? In this concrete situation (i.e. o = 0.05 and )o = 2), calculate the type-II error when A = 3 and n = 10 as well as n = 25. (c) Decide whether there exists a UMP level-a test for testing Ho : A = No VS. H1 : X # Xo. Explain your reasoning

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