A bank with branches located in a commercial district of a city and in a residential district has the business objective of developing an improved process for serving customers during the noon-to-1 P.M. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the time 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 at each branch. Complete (a) through (e) below.
Commercial
4.11
5.56
3.06
5.36
4.81
2.52
3.51
3.32
4.52
6.11
0.26
5.18
6.68
6.06
3.53
Residential
9.53
5.87
8.09
5.88
8.56
3.56
8.02
8.75
10.72
6.73
5.37
4.09
6.45
9.77
5.35
Assuming that the population variances from both banks are not equal, is there evidence of a difference in the mean waiting time between the two branches? (Use α=0.1.) Determine the hypotheses.
Let μ1 be the mean waiting time of the commercial district branch and μ2 be the mean waiting time of the residential district branch.
A. Determine the Test Statistic: tSTAT=_____ (round to 4 decimal places)
B. Determine Critical Values: (round to 4 decimal places)
C. Choose the correct conclusion:
a. Do not reject H0. There is insufficient evidence that the means differ.
b. Reject H0. There is sufficient evidence that the means differ.
c. Do not reject H0. There is sufficient evidence that the means differ.
d. Reject H0. There is insufficient evidence that the means differ.
D. Which of the following is the best interpretation of the confidence interval?
A. One can conclude with 90% confidence that the difference between the population mean wait times of the two branches falls outside this interval.
B. One can conclude with 90% confidence that the difference between the sample mean wait times of the two branches falls inside this interval.
C. One can conclude with 90% confidence that the difference between the population mean wait times of the two branches falls inside this interval.
D. One can conclude with 90% confidence that the difference between the sample mean wait times of the two branches falls outside this interval.
E. Assuming equal variances between the two populations yields a tSTAT test statistic of -4.0105 and a p-value of 0.000409. How do these results compare to the results found in (a)?
A. Assuming equal population variances results in the same tSTAT test statistic, which means that whether or not the variances are equal will not have any effect on the tSTAT test statistic under any circumstances.
B. Observing a difference this large or larger in the two sample means is less likely if you assume equal population variances than if you assume unequal variances, but the null hypothesis would be rejected either way.