Question

For each of the following two-samples t-tests (problems 1-6): (a) Determine if a F test for the ratio of two variances is appropriate to calculate for the context. If it is appropriate, conduct the analysis and report the result. Include what statistical conclusion you should draw from the analysis (i.e., whether you should conduct a pooled-variance t-test or an unequal-variances t-test). (b) Identify the most appropriate t-test to conduct for the situation/data given. Don’t forget to consider if the context requires one/two-tail tests. (c) Provide a statistical and practical interpretation of your findings.

1. A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the 12-1pm lunch period. Management decided 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 and stored in Bank1. Suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the 12-1pm lunch period. Data are collect from a random sample of 15 customers and stored in Bank2. Can we conclude the wait times are different at the two branches? (Use a 0.05 level of significance)

Waiting Time 1
7.48
3.86
7.18
6.72
7.18
6.15
8.35
9.46
7.26
5.41
7.86
4.72
9.13
5.46
8.71
Waiting Time 2
4.56
4.84
6.61
9.95
8.28
5.21
4.5
3.91
5.63
6.77
4.84
3.44
5.19
3.88
3.67

Answer 1

Data:

A.

Yes, we should conduct an F-test for the equality of variances as we would want to know the appropriate t-test applicable to the data.

i.e. we can consider the variances of the two populations to be equal and hence we will conduct a pooled variance t-test.

B.

Independent sample t-test (Pooled variable)

The hypothesis test will be two-tailed as given below:

C.

df = n1+n2 - 2

= 28

p-value = 0.1573 > 0.05 i.e. we fail to reject H0 and hence we can not claim that the wait times are different at the two branches.

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