Question

An industrial engineer at an appliance repair company compared a new strategy for dispatching its service technicians to its usual way. The new strategy consisted of using software to solve the vehicle routing problem (a mathematical program) each morning after several service calls came in. The old way was to simply wait for a service request, then send any available technician. Each of the thirty-six technicians was assigned to either the old or new way, so that there were exactly eighteen in each group. The company carried out this experiment over 40 working days, and the average daily mileages for the thirty-six repairpersons are below.

Old

99.1	99.7	94.6	70.2	101.7	88.2	63.9	109.5	97.1
182.9	193.2	95.1	92.4	105.3	85.6	89.5	92.9	87.3

New

95.8	85.2	79.3	62.2	87.9	97.9	89.3	98.6	88.6
101.1	90.1	84.1	82.2	96.6	99.7	86.7	91.5	83.2

a) Make boxplots, probability plots, and run Anderson-Darling and Shapiro-Wilks tests to check for normality. Is the normality assumptions in question Explain.
b) If you think the normality assumptions are violated, you need to run some other kind of test, like a nonparametric test. One reasonable choice would be the Mann-WhitneyWilcoxon rank sum test. Use R to run this test. Provide your code, output, and remarks in your solutions.

Answer 1

WORKSHEET 1

Summary Report for old, new

WORKSHEET 1

Probability Plot of old Shapiro-Wilks tests

WORKSHEET 1 Shapiro-Wilks tests

Probability Plot of new