A bank has the business objective of improving the process for servicing customers during the noon-to-1PM 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. A random sample of customers at two different branches of the bank is selected and the waiting times are collected and stored in the file BankTimes.xlsx. Download BankTimes.xlsx.Is there evidence that the mean waiting time in Branch 1 is less than in Branch 2?

Branch1	Branch2
7.77	2.93
2.62	1.71
8.8	6.05
9.4	8.37
4.55	9.46
8.52	5.14
3.74	4.85
4.57	3.75
8.1	9.59
5.46	9.89
3.47	5.04
2.89	8.76
4.91	12.63
5.17	0
4	3.15
5.61	7.91
1.78	5.86
7.03	9.01
2.72	7.86
1.95	9.16
6.52	3.89
4.13	11.36
4.14	3.34
3.4	7.55
8.17	5.76
5.37	6.35
6.55	4.83
3.19	9.87
3.76	9.43
8.88	10.66

1. Specify the null hypothesis and the alternative hypothesis. State whether you are using a one- or two-tailed test and explain your reasoning.

2. Determine the appropriate hypothesis test to this problem. Justify your answer.

3. Conduct calculations by hand to compute the critical value and p-value of the test. Determine your decision using two methods, the rejection region and the p-value approach.

4. Use R to conduct the hypothesis test. Copy and paste the command and output generated by R.

5. Communicate the results of the test in plain English including the meaning of the p-value.