(6 points) A random sample of students is selected from a local college, and their commute times from home to school (in minutes) are recorded and shown below. 11 11 12 12 12 12 12 12 13 13 14 15 15 16 19 19 19 19 22 22 23 23 24 25 25 26 Suppose that we want to test whether the median commute time is longer than 12 minutes with the signed rank test. Part A Calculate the absolute difference between each commute time (x) and the hypothesized median (Mo) Note: 1. The absolute differences, |x M0|, are separated by commas. 2. Remove any absolute differences having zero value. 3. For example, data = {3, 8, 9, 10, 13) and M0 = 10, then Ix M0| = {7,2,1,0, 3). So, you enter 7,2,1,3 in the textbox. Ix MOI = 1,1 ,1,1,2,3,3,4,7,7,7,7,10,10,11,11,12,13,13,14 Part B Determine the rank of the absolute differences in Part A 1. The ranks of the absolute differences are separated by commas. 2. For example, Rank = {4, 2, 1, 3}. So, you enter 4, 2, 1, 3 in the textbox. Rank of Ix M0] = 2.5,2.5,2.5,2.5,5,6.5,6.5,8,10.5,10.5,10.5,1 0.5,13.5,13.5,15.5,15.5,17,18.5,18.5,20 Part C Use the ranks you calculated in Part B to calculate the following statistics: W+ = 205 W_ = 5 E[W+] assuming H0 is true = 105 SD[W+] = 26.78619047 Round SD[W+] to 8 decimal places Part D Approximate the p-value of W+ using a Normal distribution by completing the follow: 1. Determine the z-score: 3.7333 Round the z-score to 4 decimal places 2. Determine the p-value: C] Round the p-value to 4 decimal places