Question

Branch 1 (u) 4.21 5.55 A bank with a branch (Branch 1) located in a commercial district of a city has developed an improved process for serving customers during the noon-to-1 p.m. lunch period. The waiting time (operationally defined as the time elapsed 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 15 customers is selected and the results in minutes) are shown in the table on the left. In addition, suppose that another branch (Branch 2), located in a residential area, is also concemed with the noon-to-1 p.m. lunch period. A random sample of 15 customers is selected and the results are shown in the table on the left. Assuming that the population variances from both branches are equal, is there evidence of a significant difference in the mean waiting time between the two branches? Use alpha=0.01. 3.02 5.13 4.77 2.34 3.54 3.20 4.50 Solve this question using Excel. State the null & alternative hypotheses clearly. Interpret the Excel output and state your conclusion clearly. Provide all your results and comments on this sheet. Specifically, type in your answers in the spaces provided below: mm 9 Branch 2 (uz) 9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35 10.49 6.68 5.64 4.08 6.17 9.91 5.47 Please watch the videos (in Excel Lab 2.2a and Excel Lab 2.2b) related to hypothesis testing with two samples prior to attempting this question. Are the samples related (i.e. dependent) or independent? 6.10 Null Hypothesis: 0.38 5.12 6.46 6.19 3.79 Alternative Hypothesis: mm 990 9 Interpretation of Excel output (Conclusion of Hypothesis test): Business implications: m

Answer 1

Claim Is there evidence of a significant difference in the mean waiting time between the two branches at alpha = 0.01 samples are independent. # Null hypothesis : ul = u2 # Alternative hypothesis: ul #u2 Assuming population variances for both the branches are equal DATA > Data Analysis > t - Test Two Sample Assuming Equal variances

t-Test: Two-Sample Assuming Equal Variances Branch1 4.686666667 1.73442381 Branch 2 7.114666667 4.335512381 15 15 3.034968095 Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 28 -3.816825008 0.000342595 2.467140098 0.000685191 2.763262455 test statistics -3.816825008 p value 0.000685191 critical value 2.763262455 decision : we reject Ho if p value is less than alpha value using p value approach here p value is less than alpha value we reject Ho Conclusion: there is sufficient evidence to conclude that there is a significant difference in the mean waiting time between the two brances at 1% level.

Business implication : both branches have the service are the different in their mean .