The regional manager of a bank wants to determine whether average waiting times at two branches are different. A sample of 127 customers from Branch 1 shows mean waiting time of 7.45 minutes with a standard deviation of 1.87 minutes. A sample of 114 customers from Branch 2 shows mean waiting time of 8.74 minutes with a standard deviation of 2.06 minutes.

1. Suppose that the confidence interval for the mean waiting time of Branch 1 minus the mean waiting time of Branch 2 is (-1.384, -.529) (note this is not the correct answer), then write a short interpretation of what this confidence interval means in the context of this problem. Justify your answer.