1. (Exercise 8.5.1 from edition 8 of the textbook) Let X₁, X2, ..., X20 be a random sample of size 20 from a distributio

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1 Exercise 8 5 1 From Edition 8 Of The Textbook Let X X2 X20 Be A Random Sample Of Size 20 From A Distributio 1 (69.69 KiB) Viewed 30 times

1. (Exercise 8.5.1 from edition 8 of the textbook) Let X₁, X2, ..., X20 be a random sample of size 20 from a distribution that is N(0,5). Let L(0) represent the joint pdf of X₁, X2,..., X20. It is desired to test Ho: 0 = 1 against H₁ : 0 = 0 with = {0 | 0 = 0,1}. (a). Show that L(1)/L(0) ≤ k is equivalent to x ≤ c. (b). Find c so that the significance level is a = 0.05. Compute the power of this test under H₁. (c). If the loss function is such that L(1, 1) = L(0,0) = 0 and L(1,0) = L(0, 1) > 0, find the minimax test. Evaluate the power function of this test at the points 0 = 1 and 0 = 0, respectively.