Question

Please show me how to use R to solve the problem. thanks!

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 P.M. lunch period. The bank has the business objective of reducing the waiting time (defined as the number of minutes that elapse from when the customer enters the line until he or she reaches the teller window) to increase customer satisfaction. A random sample of 15 customers is selected and waiting times(in minutes) are collected and stored in the Bank 1 column. Another branch, located in a residential area, is also concerned with the noon-to-1 p.m. lunch period. A random sample of 15 customers is selected and waiting times  (in minutes) are collected and stored in the Bank 2 column.

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.)

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

c.Construct and interpret a 95% confidence interval estimate of the difference between the population means in the two branches.

Observation	Bank1	Bank2
1	4.21	9.66
2	5.55	5.9
3	3.02	8.02
4	5.13	5.79
5	4.77	8.73
6	2.34	3.82
7	3.54	8.01
8	3.20	8.35
9	4.50	10.49
10	6.10	6.68
11	0.38	5.64
12	5.12	4.08
13	6.46	6.17
14	6.19	9.91
15	3.79	5.47

Answer 1

(b) P-value = 0.00029. This means that there is a 0.029% chance that I will mistakenly reject the claim that there is no difference in the mean waiting time between the 2 branches.

(c) Interpretation: If repeated samples are taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population mean difference of waiting times of the 2 branches between 4.29 minutes and 7.11 minutes.