2. Let X1,..., X10 be a random sample of n = 10 from a normal distribution N(0,02). (a) Find a best critical region of size 0.05 for testing Hoo21, H₁:0² = 2. : (b) Deduce the power of the test in part (a), that is, compute the power function K(2). Feel free to use any computing language to help you compute the power. (c) Find a best critical region of size 0.05 for testing Hoo² 1, H₁ : 0² = 4. (d) Deduce the power of the test in part (c), that is, compute the power function K(4). (e) Find a best critical region of size 0.05 for testing where σ > 1. Hoo² = 1, H₁:0² = 0², (f) Find a uniformly most powerful test and its critical region of size 0.05 for testing Ho: 0² = 1, H₁:0² > 1.

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