use the Wilcoxon rank-sum test. Clinical Trials of Lipitor ?The sample data below are changes in LDL cholesterol levels in clinical trials of Lipitor (atorvastatin). It was claimed that Lipitor had an effect on LDL cholesterol. (The data are based on results given in a Parke-Davis memo from David G. Orloff, M.D., the medical team leader for clinical trials of Lipitor. Pfizer declined to provide die author with the original data values.) Negative values represent decreases in LDL cholesterol. Use a 0.05 significance level to test the claim that for those treated with 20 mg of atorvastatin and those treated widi 80 mg of atorvastatin, changes in LDL cholesterol have the same median. What do the results suggest? Group treated with 20 mg of atorvastatin: ?28 ?32 ?29 ?39 ?31 ?35 ?25 ?36 ?35 ?26 ?29 ?34 ?30 Group treated with 80 mg of atorvastatin: ?42 ?41 ?38 ?42 ?41 ?41 ?40 ?44 ?32 ?37 ?41 ?37 ?34 ?31

Solution 7BSC Step 1 : Given, The given data is changes in LDL cholesterol levels taken randomly, so the observations from the same population. Hence first requirement of the Wilcoxon Rank-Sum test satisfied. Each samples contains 13 values of the changes in LDL cholesterol level of group treated with 20 mg of Atorvastatin and 14 values of the changes in LDL cholesterol level of group treated with 20 mg of Atorvastatin , it satisfies the second condition that the each sample should have the same median. Therefore, both the requirements of the Wilcoxon Sum-Rank test satisfies. Hypothesis : H : The median of changes in LDL cholesterol level of group treated with 20 mg of 0 Atorvastatin is equal to the changes in LDL cholesterol level of group treated with 80 mg of Atorvastatin H 1 The median of changes in LDL cholesterol level of group treated with 20 mg of Atorvastatin is not equal to the changes in LDL cholesterol level of group treated with 80 mg of Atorvastatin Step 2 : We have 27 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, Highest value is 44 which is assigned the rank 27. Ranks for LDL cholesterol levels of the group treated with 20 mg of Atorvastatin are 4, 10.5, 5.5, 20, 8.5, 14.5, 2, 16, 14.5, 3, 5.5, 12.5, 7. The sum of the ranks for LDL cholesterol levels of the group treated with 20 mg of Atorvastatin = 123.5