Suppose that X represents a single observation from the distribution given by:
f(x; θ) = θ*x^(θ - 1) for 0 < x < 1
a.) Find the most powerful test with significance level alpha = 0.05 to test H_0: θ = 2 against H_a: θ = 1
b.) How does the nature of the test statistic and rejection region for the most powerful test change if the Ha is changed to Ha: θ = 4.
I believe that this problem deals with the Neyman-Pearson Lemma, so I would have to find
L_0 and L_1
so, for part (a):
L_0 = pi summation from i = 1 to n of θ*x^(θ - 1) = (θ^n)*Σx^(θ - 1) I think
L_1 would equal the same thing, except theta would be theta sub 1 and in L_0, theta is theta sub 0.
Then, you would do: L(1) / L(2)
But, before I go ahead and calculate that, I am wondering if I am doing this problem correctly?