Question

A bank branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1 p.m. lunch period. To do so, the waiting time (defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. Another bank in the area is also concerned with the noon-to-1 PM lunch period. A random sample of 15 customers is selected from each bank and the waiting times are as follows:

Bank 1	4.23	5.54	3.02	5.13	4.77	2.34	2.54	3.20	4.50	6.10	0.38	6.12	6.46	6.19	4.79
Bank 2	9.66	1.90	8.02	2.79	8.73	3.82	6.01	8.35	11.49	6.68	5.64	4.08	6.17	9.91	5.47

Is there evidence of a difference in the variability of the waiting time between the two branches with an Alpha of .10?

A) What test should be run?

B) State the null and alternate hypothesis

C) Compute the value of the test statistic

D) Calculate the P-Value

E) What is your decision regarding the null hypothesis? Interpret the result.

Answer 1

For bank 1

s1 = 1.745

For bank 2

s2 = 2.768

A) We will F-test

B) H₀:

    H₁:

C) The test statistic F = s1^2/s2^2

                                  = (1.745)^2/(2.768)^2

                                 = 0.397

D) P-value = 2 * P(F < 0.397)

                   = 2 * (1 - P(F > 0.397))

                   = 2 * (1 - 0.9582)

                  = 0.0836

E) Since the P-value is less than the significance level(0.0836 < 0.1), so we should reject the null hypothesis.

At 0.10 significance level, there is sufficient evidence to conclude that there is a difference in the variability of the waiting time between the two branches.