A bank with a branch located in a commercial district of a city has developed an improved process for serving customers during the noon-to-1 pm lunch period. The waiting time (defined as the time elapsed from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. Before the implementation of the process, a random sample of 7 customers was selected and recorded their times (in minutes). After the implementation, because could not ask for the same 7 customers to come back and do their transactions again, therefore another 9 customers were randomly sampled instead and also recorded down their waiting times. The results are:

Before After

1.73 1.87

1.841.78

1.912.13

1.672.10

1.822.21

1.861.87

1.751.98

2.07

2.02

(a)Provide two reasons if you want to solve question using Wilcoxon Rank Sum test rather than t-test, and provide one reason for not choosing Wilcoxon Signed Rank test. [3]

(b)Do we have enough evidence to conclude the improved process shortens the waiting time? Use = 0.05. Partially conduct the Wilcoxon Rank Sum test using SGC, and use the rank sum to make conclusion. [5]

(Advice: Find the rank sums by hand.)

(c)Using appropriate normal probability plots and boxplots, comment whether Rank Sum test should be used for this question. If not, which test is the appropriate one?