Question

	Set A	Set B
	0.94	1.113
2	0.89	1.16
3	0.858	1.175
4	1.08	1.155
5	1.19	1.161
6	1.33	1.15
7	1.28	1.14
8	1.11	1.185
9	1.14

A) Calculate the expected value of the Wilcoxon Rank-Sum test Statistic E(Wx) assuming the null hypothesis of equal medians being true

B) Conduct a Wilcoxon Rank sum test on the data

Answer 1

Wilcoxon Rank - Sum test statistic is given by u - u z = - ~ N(0,1) distribution. where, u= ni+ M2 (2+1) –T u = E(u) = nim } = v(u) = nie (nitr+1) 12 The appronimation is good if both n, & in greater than 8. are A) Calculate the expected value of the wilcoron Rank- sum test is given by E ( Wx) = = nim 2 z here , & Na is 988 ie nie og M = 08 respectively 2 E(Wx) = 9x8 = 12 = 36 The expected value of the wilcoxon Rank-sum test is 36. V(Wx) = n, n2 (n + H₂+1) 9X8 (1) 12 2- - 108

e B) Wilcoxon Rank sum test on the given data. (Y) Set B 1.113 1.175 1.155 Sample Set A (x). 10.94 0.89 0.858 1.08 1,19 6 1.33 7 1.28 8 1.11 9 1.14 1.161 115 1.185 Wilcosoon Rank sum test statistic is given by u s - ~ NCoil) z = 0 u= n, n2 + M2 (1271) -T. 2 where T= the sum of ranks of the Y'S (set B) in the combined ordered sample. The combined ordered sample is given by 0.858 0.89 0.94 1.08 1 1.113 114 114 1.15 1.155 1.16 1.161 1.175 1.185 119 1,28 1.33 Rank or above ordered sample is 1 2 3 4 sex 5 6 7.5 7.5 9 10 (*) (*) (*) ( Cy) (%) (Y) (Y) (Y) 11 12 13 14 15 16 17 (Y) (y) (y) (y) (x) (*) (*)

T = 6 + 7.5 + 9+10+ 11+ 12 +13 + 14. = 82.5 0,=9 22=8 u= sint 92 (821) _T u= 9x8+ 8(90 – 82.5 2 82.5 = 72 + = 72 +36 - 82.5 Tu=25.5 Test statistic is given by, u-E(U) ~ N(Oil) Z= Jucu N 25.5-36 108 - 10.5 - = -1.0103 63442 2 = 10.39230 - Cal 12l = 1.010363442 Tab 2 = 18 Conclusion, Caltzl < Tabz Accept Ho at 51, level of significance.