Question 5 Let X1, X2, X3, X4 be a random sample of STAT2001 scores, assumed to be n(ux, ox), and let Y1, Y2, Y3, Y4, Y's be a random sample STAT2006 scores, assumed to be n(My, or). Suppose X1, X2, X3, X4, Y1, Yz, Y3, Y4, Y's are independent, and the following data are observed: X1 = 75, X2 = 95, X3 = 80, X4 = 65py1 = 80, y2 = 75, y3 = 90, y4 = 70, y5 = 70. (a) Find a 95% confidence interval for ox. [4] (b) Find a 95% confidence interval for . [4] (c) Find the distribution of (X1-X2)2/ox (Y1-Y2) 2/07 [4] (d) Based on the result in (c), construct an alternate 90% confidence interval for * [4] (e) Is the confidence interval in (b) better than the one in (d)? State your reasons. [4]