Computational Statistics

The management at New Century Bank claims that the mean waiting time for all customers at its branches is less than that at the Public Bankr which is its main competitor. A business consulting rm took a sample of 20? customers from the New Century Bank and found that they waited an average of 4.40 minutes before being served. Another sample of 297 customers taken from the Public Bank showed that these customers waited an average of 4.65 minutes before being served. Assume that the standard deviations for the two populations are 1.22 and 1.49 minutes, respectively. Let p. be the mean waiting time for all customers at New Century Bank, and 312 be the mean waitingtime for all customers at the Public Bank. a. Make a 98% con dence interval for the difference between the two population means. Round your answers to two decimal places. b. Test at a 2.5% signicance level whether the claim of the management of the New Century Bank is true. Round your answer to two decimal places. Conclusion: Hg. Co nclude that the mean waiting time for all customers at New Century Bank branches is that at the Public Bank. The bank's claim is . thesameas less than :2. Calculate the p-value for the test of part b. Based on this p-value. would you reject the null hypothesis if a = 0.01 ? What if a = 0.05? Round your answer to four decimal places. Fora = 0.05, we H0