Let X1, X2, , X10 be a random sample of size ten from the Normal(3, σ2) distribution.
(a) Use the likelihood ratio test to derive a 5%-level critical region for testing H0 : σ2 = 1
versus H1 : σ2 ≠ 1.
(b)Suppose the following ten values from the Normal(3, σ2) distribution are observed. Do we
reject the null hypothesis H0 : σ2 = 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
.