Using the Mann-Whitney UTest ?The Mann-Whitney ?U?test is equivalent to the Wilcoxon rank-sum test for independent samples in the sense that they both apply to the same situations and always lead to the same conclusions. In the Mann-Whitney ?U? test we calculate Use the pulse rates listed in Table 13-5 in this section to find the 2 test statistic for the Mann-Whitney ?U? test. Compare this value to the ?z? test statistic found using the Wilcoxon rank-sum test. where

Solution 13BB Step 1 : T he pulse rates of the males and females are given below Step 2 : We have 23 observations, based on the values we give ranks, if it is least value then rank will be 1 and next to the value will be 2 and so on. If there is a tie then mean of the values is the rank, Ranks for sample 1 are 4.5, 11, 19, 1, 20.5, 17, 7, 9, 9, 2.5, 17, 6 The sum of the ranks for sample 1 = 123.5 Test statistic is given below n1 1 U 2 Z = 1 2 1n2+n +1) 12 Where, n1 = number of male samples = 12 and n2 be the number of female samples = 11 (n +n +1) U =n n1 2 1 2 -R 12 n1(+n +1) U =n n1 2 2 -R =(12)(11)+ 12(+12+1)-123.5 2 = 210-123.5 = 86.5 And 1n U 2 Z = n1 2 1 2n +1) 12 86.5 1* 12 = 2 1* 11212+11+1) 20.5 = 264 = 0.07765