Suppose that X1, X2,..., Xn1 , Y1, Y2,..., Yn2 , and W1, W2,..., Wn3 are independent

QUESTION:

Suppose that X1, X2,..., Xn1 , Y1, Y2,..., Yn2 , and W1, W2,..., Wn3 are independent random samples from normal distributions with respective unknown means 1, 2, and 3 and variances 2 1 , 2 2 , and 2 3 . a Find the likelihood ratio test for H0 : 2 1 = 2 2 = 2 3 against the alternative of at least one inequality. b Find an approximate critical region for the test in part (a) if n1, n2, and n3 are large and = .05.