Question 3. A company is in the process of deciding whether to purchase a maintenance contract for its new manufacturing system. Managers fell that maintenance expense should be related to usage and have collected a data set on weekly usage(X, in hours) and annual maintenance expense(Y, in thousands of dollars). The summary statistics are: n n n X, 7 Z = 25.193333, 2X3 2 1.906442 x 104, 2(X, X)2 = 23.298667, TL i=1 n 2] \" 51.71663, 21/? = 8.037965 x 104, 20/,- 17)2 = 141357702, 21: 12:1 i=1 n = 30, XX; = 3.913961 x 104, 2(X, XMY; Y) = 52.180184, 221 b0 2 4.706889, bl = 2.239621, MSE = 0.874781. Assume the simple linear regression model(Y : ,80 + ,81X + E) is plausible. (1) [1 Mark] Find 3(b1). (2) [1 Mark] Find a 95% condence interval for 31. (3) [4 Marks] Carry out a test of hypotheses at level 0.05 to decide Whether [81 = 0, using ttest and the rejection region approach