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 Bank, which is its main competitor. A business consulting firm took a sample of 200 customers from the New Century Bank and found that they waited an average of 4.5 minutes before being served. Another sample of 300 customers taken from the Public Bank showed that these customers waited an average of 4.75 minutes before being served. Assume that the standard deviations for the two populations are 1.2 and 1.5 minutes, respectively.
a. Make a 97% confidence interval for the difference between the two population means.
b. Test at a 2.5% significance level whether the claim of the management of the New Century Bank is true.
c. Calculate the p-value for the test of part b. Based on this p-value, would you reject the null hypothesis if α = .01? What if α = .05?