Show that Summation i 1 n yi mu02 Summation i 1 n yi y2

Show that Summation i = 1 n (y_i - mu_0)^2 - Summation i = 1 n (y_i - y)^2 = n (y - mu_0)^2 Use the result of (a) to find the critical region of the likelihood ratio test (alpha = 0.05) for testing the null hypothesis H_0 : mu = mu_0 against the alternative H_a : mu mu_0 on the basis, of a random sample of size n from a normal population with known variance sigma^2. Determine the least squares line for the point (0, 2), (1, 3), (4, 5), (7, 6).

Solution