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 lonas made. A random sample of seven Ohio banks is selected. The bad debt ratios (written as percentages) for these banks are 7,4,6,7,5,4, and 9 percent.
a) The mean bad debt ratio for all federally insured bank is 3.5%. Federal banking officials claim that the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks. Set up the null and alternative hypotheses that should be used to statistically justify this claim.
b) Assuming that bad debt ratios for Ohio banks are normally distributed, use the sample results given above to test the hypotheses you set up in part (a) with alpha=0.01.
c) Use the above sample to calculate a lower one-sided 95% confidence interval for the mean bad debt ratio for Ohio banks. Use this interval to test the hypotheses you se up in part (a) with alpha=0.01.
d) What do the results of parts (b) and (c) say about whether or not the mean bad debt ratio for Ohio banks is greater than the average for all ffederally insured banks?