a bank a branch location a commercial district we city developed improved proces

Question

a bank a branch location a commercial district we city developed improved process serving customers noon-to 1 pm. lunch period. the waiting time (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 stored in Bank 1), and the results (in munities) are as follows: 4.21 5.55 3.02 5.13 4.77 2.34 3.54 4.5 6.1 0.38 5.12 6.46 6.19 3.79 Suppose that another branch, located in a residential area, is also concerned with the noon-to1 pm. Lunch period A random sample of 15 customers is selected (and stored in Bank 2), and the results (in minutes) are as follows: 9.66 5.9 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 A. Is there evidence of a difference in the variability of the waiting time between the two branches? (use a=0.05) B. Determine the P value in (a) and interpret its meaning C. What assumption about the population distribution of the two banks is necessary in (a)? Is the assumption valid for these data? D. Based on the results of (a) is it appropriate to use the pooled-variance t-test to compare the means of the two branches? a bank a branch location a commercial district we city developed improved process serving customers noon-to 1 pm. lunch period. the waiting time (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 stored in Bank 1), and the results (in munities) are as follows: 4.21 5.55 3.02 5.13 4.77 2.34 3.54 4.5 6.1 0.38 5.12 6.46 6.19 3.79 Suppose that another branch, located in a residential area, is also concerned with the noon-to1 pm. Lunch period A random sample of 15 customers is selected (and stored in Bank 2), and the results (in minutes) are as follows: 9.66 5.9 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 A. Is there evidence of a difference in the variability of the waiting time between the two branches? (use a=0.05) B. Determine the P value in (a) and interpret its meaning C. What assumption about the population distribution of the two banks is necessary in (a)? Is the assumption valid for these data? D. Based on the results of (a) is it appropriate to use the pooled-variance t-test to compare the means of the two branches?

Explanation / Answer

a) Calculating the t-statistic and looking at the student t-distribution table we can reject the null hypothesis and say that there is a significant difference in the mean time.

b) p value comes out to be 0.068. Now usually a value of < 0.05 is taken as a safer side value i.e. when it is safe to reject the null hypothesis. But a 5-10% can also be taken.So we can interpret the overall it is significant.

C) The assumption necessary is that population of the banks is normally distributed with 0 mean and constant variance. Yes in this case the assumption is valid. The data is normally distributed.

Only thing is the sample size is small. So it is better to use a student t-distribution.

d) There is a significant mean difference as seen from a) and also the sample size is less than 30(in this case it is15). So it is appropriate to use pooled variance t test to compare the means of the two branches.

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