Question

A bank with branches located in a commercial district of a city and in a residential area has the business objective of developing an improved process for serving customers during the​ noon-to-1 P.M. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window. Data are collected from a random sample of 15 customers at each branch.

Commercial	Residential
4.35	9.88
5.54	5.77
3.01	8.06
5.24	5.79
4.76	8.64
2.34	3.58
3.64	8.12
3.24	8.63
4.44	10.46
6.16	6.55
0.14	5.56
5.17	4.15
6.46	6.13
6.37	9.88
3.55	5.27

a. Assuming that the population variances from both banks are​ equal, is there evidence of a difference in the mean waiting time between the two​ branches? (Use α=0.05.​).

Let μ1 be the mean waiting time of the commercial district branch and μ2 be the mean waiting time of the residential area branch. Determine the hypotheses.

b. Find the test statistic. (Round to two Decimal places)

c. Find the Critical Values. (Use a comma to separate answers as needed. Round to two decimal places)

d. Determine the p-value in (a) and interpret its meaning.

e. Construct and interpret a 95​% confidence interval estimate of the difference between the population means between the two branches. (Round to three decimal places.)

Answer 1

using excel>addin>phstat>two sample test

we have

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data		Confidence Interval Estimate
Hypothesized Difference	0		for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample			Data
Sample Size	15		Confidence Level	95%
Sample Mean	4.294
Sample Standard Deviation	1.706172827		Intermediate Calculations
Population 2 Sample			Degrees of Freedom	28
Sample Size	15		t Value	2.0484
Sample Mean	7.098		Interval Half Width	1.4534
Sample Standard Deviation	2.154109693
			Confidence Interval
Intermediate Calculations		Interval Lower Limit	-4.2574
Population 1 Sample Degrees of Freedom	14		Interval Upper Limit	-1.3506
Population 2 Sample Degrees of Freedom	14
Total Degrees of Freedom	28
Pooled Variance	3.7756
Standard Error	0.7095
Difference in Sample Means	-2.8040
t Test Statistic	-3.9520
Two-Tail Test
Lower Critical Value	-2.0484
Upper Critical Value	2.0484
p-Value	0.0005
Reject the null hypothesis

a.Let μ1 be the mean waiting time of the commercial district branch and μ2 be the mean waiting time of the residential area branch. the null and alternative hypothesis are

Ho:μ1 =μ2

Ha:μ1 μ2 (two tailed)

b. the test statistic t = -3.95

c. Find the Critical Values are (-2.05 ,2.05)

d. the p-value is 0.0005 . since p value is less than 0.05 so we reject Ho and conclude that there is a difference in the mean waiting time between the two​ branches

e. 95% Confidence interval is (-4.257,-1.351)

we are 95​% confident that the difference between the population means between the two branches lies between (-4.257,-1.351)