Likelihood ratio for variance:

2. Likelihood ratio for variance. Suppose that we have data X1, ..., X, " N(0, v) (here v is the variance), and we are testing Ho : v = 1 against H1 : v # 1. (a) Compute the MLE i. (b) Construct the generalized likelihood ratio statistic A for this test. Then calculate -2log(A), simplified into a clean form. You should be able to write it without any Xy's in the final answer, only i and constants such as e, n, etc. (c) Suppose you observe data X1, ..., X, for sample size n = 40 with these summary statistics: sample mean X = 0.8, sample variance $2 = 0.9. What is the value of -2 log(A), for this data? (d) Perform a x2 test (i.e. calculate a p-value-you can use the table in the back of the book)