Suppose that X represents a single observation from the distn given by f(x; theta) = theta*x^(theta - 1) for 0 < x < 1
Find the most powerful test with significance level alpha = 5% to test Ho: theta = 2 against Ha: theta = 1.
How does the nature of the test statistic and rejection region for the most powerful test change if the Ha is changed to Ha: theta = 4.