15.5.2 Two samples of sizes m = 20 and n = 10, respectively, are selected from two populations. Let T I , . . . ,~ 1 0 d,e noting the numbers of observations from the first sample that do not exceed the lcth (k = 1, . . . , 10) element in the ordered second sample, be 1, 1,2,4,4,6,8,9,11d, . (i) Find the value of Wilcoxon and Mann-

Whitney statistic as a function of

d. (ii) Find the value of Kolmogorov-Smirnov statistic as a function of

d. (iii) Suggest the appropriate alternative hypothesis, and determine d for which the hypothesis about the same median can be rejected based on the Mann-Whitney or Wilcoxon test. (iv) Answer (iii) using the Kolmogorov-

Smirnov test.