Question

Wells Fargo claims that the waiting time for its customers is the lower than at Bank of the West. You draw random samples of 30 customers at each bank. At Wells Fargo, the mean waiting time is found to be 5.3 minutes, with a standard deviation of 1.1 minutes. At Bank of the West, the mean waiting time is found to be 5.6 minutes with a standard deviation of 1.2 minutes. Test Wells Fargo’s claim at a 0.05 significance level. Let population 1 be Wells Fargo customers and population 2 be Bank of the West customers.

a) State the null and alternative hypotheses.

b) Find the value of the test statistic. You may use a graphing calculator. Round to three decimal places.

c) Find the P-value. You may use a graphing calculator. Round to three decimal places.

d) State whether you should reject or fail to reject the null hypothesis. Justify your answer.

e) State your conclusion in non-technical terms.

f) To construct a confidence interval for ?1 − ?2 that corresponds to this hypothesis test, what confidence level should you use? (90%, 95%, 99%, for example – a sketch may help)

g) Construct this confidence interval. You may use a graphing calculator. Round to three decimal places.

h) Explain why you reach the same conclusion with the confidence interval and the hypothesis test.

Answer 1