Let X1,X2,X3,X4 be a random sample of STAT2001 scores, assumed to be TLQJX, of), and let Y1,Y2,Y3,Y4,Y5 be a random sample STAT2006 scores, assumed to be nQuYJE). Suppose X1,X2,X3,X4,Y1,Y2,Y3,Y4,Y5 are independent, and the following data are observed: x1 = 75,962 = 95, x3 = 80, x4 = 65,y1 = 80, yz = 75,y3 = 90, 314 = 70,y5 = 70. (a) Find a 95% confidence interval for 0;. [4] 2 (b) Find a 95% confidence interval for g. Y [4] n . n . (XlXz)z/O')2{ (c) Find the distribution of (Y1_Y2)2/U%. [4] 2 (d) Based on the result in (c), construct an alternate 90% confidence interval for g. Y [4] (e) Is the confidence interval in (b) better than the one in (d)? State your reasons. [4]