Data Set A Data set B 2 Take Datasets A and B and delete dup

Data Set A

Data set B

2. Take Datasets A and B and delete duplicated values such that each value is unique even when pooling the two datasets. Just like with the previous problem, treat data sets A and B as hypothetical data on the weights of children whose parents smoke cigarettes, and those whose parents do not, respectively.

a) Calculate the expected value of the Wilcoxon Rank-Sum test statistic E(W_X)assuming the null hypothesis of equal medians being true.

b) Conduct a Wilcoxon Rank-Sum test on the data.

60.41
60.00
60.21
57.61
56.20
56.79
56.40
56.51
56.56
56.46
57.16

Solution

Wilcoxon Rank-Sum test A B Rank A Rank B 60.41 57.16 19 11 60 57.52 17 15 60.21 56.99 18 8 57.61 57.02 16 9 56.2 57.28 1 12 56.79 57.05 7 10 56.4 56.74 2 6 56.51 57.43 4 13 56.56 57.5 5 14 56.46 3 Sum 92 Expected value 95 std. error 13.41641 stat -0.22361 conclusion : the statistic value is less than the critical value , hence accep the null hypoyhesis and conclude that the medians are equal