1. A bank is experimenting with processes to improve customer service during peak periods of business (for example, during the lunch hour). Two alternative processes were implemented at two different bank branches. A random sample of 15 customers was chosen at each bank, and their waiting times were recorded. These data, and the Excel output, can be found on the excel file Bank_waiting_time.xls. Note: ignore the sample size issue.

• a) Set up the null and alternative hypotheses.

• b) Using Excel output, is there evidence that the mean waiting time for the two branches are not equal? Interpret the sample t-value and the two tailed p-value for the test.

• c) Given your answer to part b. above, which type of error are you vulnerable to, Type I or Type II? Explain in a single sentence.

• d) Are the samples for this analysis "independent samples" or "related samples"? Explain briefly.
• DATA

t-Test: Two-Sample Assuming Equal Variances
	Waiting Time branch 1	Waiting Time Branch 2
Mean	4.286666667	7.114666667
Variance	2.682995238	4.335512381
Observations	15	15
Pooled Variance	3.50925381
Hypothesized Mean Difference	0
df	28
t Stat	-4.134306277
P(T<=t) one-tail	0.00014642
t Critical one-tail	1.701130934
P(T<=t) two-tail	0.000292839
t Critical two-tail	2.048407142

Waiting Time branch 1		Waiting Time Branch 2
Mean	4.286666667	Mean	7.114666667
Standard Error	0.422925938	Standard Error	0.537618972
Median	4.5	Median	6.68
Mode	#N/A	Mode	#N/A
Standard Deviation	1.637985115	Standard Deviation	2.082189324
Sample Variance	2.682995238	Sample Variance	4.335512381
Kurtosis	0.832925217	Kurtosis	-1.056273871
Skewness	-0.832946775	Skewness	0.072493057
Range	6.08	Range	6.67
Minimum	0.38	Minimum	3.82
Maximum	6.46	Maximum	10.49
Sum	64.3	Sum	106.72
Count	15	Count	15

Waiting Time branch 1	Waiting Time Branch 2
4.21	9.66
5.55	5.90
3.02	8.02
5.13	5.79
4.77	8.73
2.34	3.82
3.54	8.01
3.20	8.35
4.50	10.49
6.10	6.68
0.38	5.64
5.12	4.08
6.46	6.17
6.19	9.91
3.79	5.47