15. Suppose that you want to test whether the returns on US Technology Sector ETFs (XLK) are the same, or different, than the returns on US Materials Sector ETFs. (XLB). You have collected 5 years of monthly data (n=60) from both ETFs. The average annual return for XLK is 27.85% and annual standard deviation of return for XLK is 17.07%. The average annual return for XLB is 25.14% and annual standard deviation of return for XLB is 19.17%. You want your test to have a 5% significance and you are testing from two independent samples. The samples come from normally distributed populationswith unknown but equal variance. Answer each of the following questions and be sure to label your answers so that I can read them and know which question you are answering. Circle your answer if the question is asking for a specific value. Show your work for each question.

a. State the hypothesis that you are testing

b. Identify the appropriate test statistic and write the formula for the test statistic

c. Calculate the degrees of freedom

d. Specify the critical value and state the decision rule

e. Compute the test statistic and make the statistical decision on whether to accept or reject the null