2. 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.
   1. Set up the null and alternative hypotheses.
   2. 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.
3. 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.
4. Are the samples for this analysis "independent samples" or "related samples"? Explain briefly.

Test:

	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

Descriptives:

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

DATA:

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