use the Wilcoxon rank-sum test. Arrival Delay Times Use the sample data given in Exercise and test the claim that arrival delay times for Flight 19 and Flight 21 have the same median. Use a 0.05 significance level. Exercise Flight 19 -5 -32 -13 -9 -19 49 -30 -23 14 -21 -32 11 Flight 21 -23 28 103 -19 -5 -46 13 -3 13 106 -34 -24

Solution 5BSC Step 1 : Given, In the above example the data consists of the arrival delay times of American Airlines Flights 19 and 21 taken randomly, so the observations from the same population. Hence first requirement of the Wilcoxon Rank-Sum test satisfied. Each samples contains 12 values of the delay times, 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 :0The median of the delay in arrival time of flight 19 is equal to the median of the delay in arrival time of flight 21. H : The median of the delay in arrival time of flight 19 is not equal to the median of the 1 delay in arrival time of flight 21. Step 2 : We have 24 observations from Flight 19 and 21. 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, for example the rank of 5 is 2.5. Highest value is 106 which is assigned the rank 24. Ranks for the flight 19 are 2.5 , 18.5 , 7 , 4, 10.5 , 22 , 17 , 13.5 , 9 , 12 , 18.5 , 5. The sum of the ranks for flight 19 = 139.5