Two samples of sizes m = 20 and n = 10, respectively, are selected from two populations. Let r1, ...,r10, denoting the numbers of observations from the first sample that do not exceed the kth (k = 1, ..., 10) element in the ordered second sample, be 1, 1, 2, 4, 4, 6, 8, 9, 11,

d. (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.