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 1.00 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) of all customers during this hour is recorded over a period of one week. A random sample of 15 customers is selected, 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 1.00 pm lunch period. A random sample of 15 customers is selected, and the results 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 5% level of significance).
b) Find the p-value in (a) and interpret its meaning.
c) What assumption is necessary in (a)? Is the assumption valid for these data?