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 form when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of 15 customers is selected (and stored in Bank 1), and the results (in minutes) are as follows:
4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20
4.50 6.10 0.38 5.12 6.46 6.19 3.79
Suppose that another branch, located in a residential area, is also concerned with the noon-to-1 pm. lunch period. A random sample of 15 customers is selected (and stored in Bank2), and the results (in minutes) are as follows:
9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35
10.49 6.68 5.64 4.08 6.17 9.91 5.47
a. Is there evidence of a difference in the variability of the waiting time between the two branches? (Use α= 0.05
b. Determine the p-value in (a) and interpret its meaning.
c. What assumption about the population distribution of the two banks is necessary in (a)? is the assumption valid for these data?
d. Based on the results of (a), is it appropriate to use the pooled-variance ttest to compare the means of the two branches?