Identify the value of the pooled-variance t statistic the usual t test based on the equal

6.3 A Nonparametric Alternative: The Wilcoxon Rank Sum Test 6.14 Set up the rejection regions for testing:

a. H

: ∆ ⫽ 0 versus H a : ∆ ⫽ 0, with n 1 ⫽ 10, n 2 ⫽ 8, and a ⫽ .10

b. H

: ∆ ⫽ 0 versus H a : ∆ ⬍ 0, with n 1 ⫽ n 2 ⫽ 7, and a ⫽ .05

c. H

: ∆ ⫽ 0 versus H a : ∆ ⬎ 0, with n 1 ⫽ 8, n 2 ⫽ 9, and a ⫽ .025

6.15 Conduct a test of H

: ⌬ ⫽ 0 versus H a : ⌬ ⬎ 0, for the sample data given here. Use a ⫽ .05. Treatment 1 4.3 4.6 4.7 5.1 5.3 5.3 5.8 Treatment 2 3.5 3.8 3.7 3.9 4.4 4.7 5.2 6.16 Refer to the data of Exercise 6.15. Place a 95 confidence interval on the median differ- ence between the two treatments ⌬. Bus. 6.17 A cable TV company was interested in making its operation more efficient by cutting down on the distance between service calls while still maintaining at least the same level of serv- ice quality. A treatment group of 18 repairpersons was assigned to a dispatcher who monitored all the incoming requests for cable repairs and then provided a service strategy for that day’s work orders. A control group of 18 repairpersons was to perform their work in a normal fashion, by providing service in roughly a sequential order as requests for repairs were received. The average daily mileages for the 36 repairpersons are recorded here: Treatment Group 62.2 79.3 83.2 82.2 84.1 89.3 95.8 97.9 91.5 96.6 90.1 98.6 85.2 87.9 86.7 99.7 101.1 88.6 Control Group 97.1 70.2 94.6 182.9 85.6 89.5 109.5 101.7 99.7 193.2 105.3 92.9 63.9 88.2 99.1 95.1 92.4 87.3

a. Various plots of the data are given here. Based on these plots, which of the test proce-

dures presented in this chapter appears more appropriate for assessing if the treat- ment group has smaller daily mileages in comparison to the control group?

b. Computer output is provided for two versions of the t test and a Wilcoxon rank sum

test the Mann-Whitney and Wilcoxon rank sum tests are equivalent. Compare the results for these three tests and draw a conclusion about the effectiveness of the new dispatcher program. Use a ⫽ .05.

c. Place a 95 confidence interval on the differences between the daily mileages for the

two groups of repairpersons. d. Does it matter which of the three tests is used in this study? Might it be reasonable to run all three tests in certain situations? Why or why not? 50 Treatment Boxplot of treatment and control groups A v erage daily mileage Control 75 100 125 150 175 200 Mann-Whitney Test and CI: Treatment, Control Point estimate for ETA1-ETA2 is –5.20 95.2 Percent CI for ETA1-ETA2 is –12.89, 0.81 W = 278.5 Test of ETA1 = ETA2 vs ETA1 ETA2 is significant at 0.0438 The test is significant at 0.0438 adjusted for ties N Median Treatment Control 18 18 88 .25 93.75 5 1 50 100 Control Normal probability plot for control group Normal 150 200

10 20

Percent 30 40 50 60 70 80 90 95 99 P -value .010 RJ .826 N 18 StDev 33.20 Mean 102.1 5 1 60 70 80 90 Treatment Normal probability plot for treatment group Normal 100 110

10 20

Percent 30 40 50 60 70 80 90 95 99 P -value .046 RJ .944 N 18 StDev 9.059 Mean 88.33