Question

A bank wants to develop an improved process for serving customers during the noon-to-1pm lunch period. Management decides to first study the waiting time of the current process. Data is collected from a random sample of 15 customer and their waiting time is recorded (in minutes) and is located in the Excel data file for this assignment under the tab bank1. For comparative purposes, similar data is collected from bank2.

Bank1:

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

Bank2:

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. Assuming that the population variances from both branches are equal, is there evidence that the mean waiting time is difference between the two banks? Under a 0.05 level of significance.

            b. Determine the p-value in part a and interpret its meaning.

            c. In addition to equal variances, what other assumption is necessary to perform the test required by part a? Do you feel this assumption is valid? Explain (prove your conclusion.)

            d. Construct and interpret a 95% confidence interval estimate of the difference between the population means of the two banks.

e. Would your answer change for problem 1 part a above if you had assumed unequal variances?  

Answer 1

Following is the output of descriptive statistics:

Descriptive statistics
	Bank1:	Bank2:
count	15	15
mean	4.2867	7.1147
sample standard deviation	1.6380	2.0822
sample variance	2.6830	4.3355
minimum	0.38	3.82
maximum	6.46	10.49
range	6.08	6.67

(a)

(b)

The p-value is: 0.0003

(c)

Since sample sizes are small so normality must be assumed.

(d)

(e)

That is decision does not change.