Probability and Statistics

Let X and Y be two independent continuous symmetric random variables with the following ordered observations: X: 5.13 8.22 11.81 14.55 15.36 23.71 Y: 6.42 8.47 9.12 12.50 14.12 16.57 (a) Let 7r be the third quartile of Y. Compute the probabil ity that 7r is contained in the interval (847,1412). (Give a precise answer in fractions.) (b) Compute the Wilcoxon's rank sum statistic W' .(c) Let mX be the median of X , and let my be the median of Y. The hypotheses are: . The null hypothesis H0: mX = my ; . The alternative hypothesis H1: To); > my ; Compute the pvalue of the Wilcoxon rank sum test, and decide if we should reject H0, given that the signicance level a: is 0.5