Let X_{1}, X_{2}, …, X_{10}be a random sample of size ten from the Normal(3, σ^{2}) distribution.

(a) Use the likelihood ratio test to derive a 5%-level critical region for testing H_{0}: σ^{2}= 1

versus H_{1}: σ^{2}≠ 1.

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

reject the null hypothesis H_{0}: 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

.