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(a) Use the likelihood ratio test to derive a 5%-level critical region for testing H0 : σ^2 = 1

versus H1 : σ^2 ≠ 1.

(b)Suppose the following ten values from the Normal(3, σ^2) distribution are observed. Do we

reject the null hypothesis H0 : σ^2 = 1 at 5%-level? Please justify your answer.

2.82, 2.35, 3.74, 1.93, 4.51, 3.17, 1.41, 4.23, 4.77, 3.89