A personnel director in a particular state claims that the mean annual income is greater in one of the​ state's counties​ (county A) than it is in another county​ (county B). In County​ A, a random...

A personnel director in a particular state claims that the mean annual income is greater in one of the​ state's counties​ (county A) than it is in another county​ (county B). In County​ A, a random sample of 15 residents has a mean annual income of 40300 and a standard deviation of 8900. In County​ B, a random sample of 8 residents has a mean annual income of  37800 and a standard deviation of 5800. At a=0.01 ​, answer parts​ (a) through​ (e). Assume the population variances are not equal. If​ convenient, use technology to solve the problem.