Exercise 10.108:Suppose that X₁, X₂, ..., X_n1, Y₁, Y₂, ..., Y_n2 and W₁, W₂, ..., W_n3 are independent random samples from normal distributions with respective unknown means ₁, ₂ and ₃ and variances ₁², ₂² and ₃².

1. Find the likelihood ratio test for H₀: ₁² = ₂² = ₃² against the alternative of at least one inequality.

2. Find an approximate critical region for the test in part (a) if n₁, n₂ and n₃ are large and = 0.05.