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Suppose that X1, X2, X3, X4 are iid N(θ,4). We wish to test H0: θ =...

Suppose that X1, X2, X3, X4 are iid N(θ,4). We wish to test H0: θ = 2 vs H1: θ = 5. Consider the following tests:

Test 1: Reject H0 iff X1 > 4.7

Test 1: Reject H0 iff 1/3(X1 + 2X2) > 4.5

Test 3: Reject H0 iff 1/2(X1 + X3) > 4.2

Test 4: Reject H0 iff x̄>4.1 (xbar > 4.1)

Find Type 1 and Type 2 error probabilities for each test and compare the tests.

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