A bank with five tellers and one queue opens its doors at 9: 00 AM, closes its d

Question

A bank with five tellers and one queue opens its doors at 9: 00 AM, closes its doors at 5: 00 PM, but stays open until all customers in the bank at 5: 00 PM have been served. Students in the simulation course collected data and ran simulations. The table below shows typical output statistics from 10 independent simulation replications for the bank, assuming that no customers are present initially. Answer the following questions: a. Obtain a 95% (one-sided) confidence interval for the average time when the last teller working can leave the bank (for example: before 5: 30pm) b. The bank claims that the average delay is 2 minutes. Test if that hypothesis can be accepted at a significance level alpha = 10% c. Create a 95% confidence interval for the variance of the proportion of customers that would be delayed 5 or more minutes.

Explanation / Answer

Excel formula (just copy & paste it on excel):

Replication Finish Time (hours) Average delay in queue (minutes) Average queue length Proportion of customers delayed < 5 minutes (a) 1 8.12 1.53 1.52 0.917 95% cofidence interval for Finish Time: 2 8.14 1.66 1.62 0.916 Upper limit 8.20605 = 8hrs 12.36299 minutes 3 8.19 1.24 1.23 0.952 lower limit 8.09395 = 8hrs 5.637015 minutes 4 8.03 2.34 2.34 0.822 Thus, the last bank teller can leave before 5:12 hrs 5 8.03 2 1.89 0.84 6 8.32 1.69 1.56 0.866 (b) 2-sided 1 sample t-test 7 8.09 2.69 2.5 0.783 H0: average delay =2 min 8 8.19 2.86 2.83 0.782 Ha: average delay not 2 min 9 8.15 1.7 1.74 0.873 t-stat= 0.176325 10 8.24 2.6 2.5 0.779 p-value= 0.863943 >.1 cant reject H0 and we conclude that average delay is 2 min only; claim is true mean 8.15 2.031 1.973 0.853 SD 0.09043107 0.555966626 0.531058691 0.062344919 (C ) C.I. for variance SE 0.02859681 0.175812084 0.167935503 0.019715194 variance follows Chi-sq distribution Upper limit 0.001839 lower limit 0.009243

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