Question

# A bank with branches located in a commercial district of a city and in a residential...

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.)

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)

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