The bad debt ratio for a financial institution is defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made. Suppose that a random sample of seven Ohio banks is selected and that the bad debt ratios (written as percentages) for these banks are 7%, 4%, 6%, 7%, 5%, 4%, and 9%.
a. Banking officials claim that the mean bad debt ratio for all Midwestern banks is 3.5 percent and that the mean bad debt ratio for Ohio banks is higher. Set up the null and alternative hypotheses needed to attempt to provide evidence supporting the claim that the mean bad debt ratio for Ohio banks exceeds 3.5 percent. Discuss the meanings of a Type I error and a Type II error in this situation.
b. Assuming that bad debt ratios for Ohio banks are approximately normally distributed, use critical values and the given sample information to test the hypotheses you set up in part a by setting a equal to .01.
c. Are you qualified to decide whether we have a practically important result? Who would be? How might practical importance be defined in this situation?
d. The p-value for the hypothesis test of part (b) can be computer calculated to be .006. What does this p-value say about whether the mean bad debt ratio for Ohio banks exceeds 3.5 percent?