Question

uppose bank officials claim that the mean bad debt ratio for all banks in the Midwest region is 3.5 percent and that the mean bad debt ratio for all Ohio banks is higher. Using the 95 percent confidence interval (given by Minitab), can we be 95 percent confident that this claim is true? Using the 99 percent confidence interval you calculated, can we be 99 percent confident that this claim is true? Explain.

Answer 1

The 95 percent confidence interval indicates that we can be 95 percent confident that the true mean bad debt ratio falls within a certain range. The 99 percent confidence interval is wider, but it does not provide more certainty about the claim made by the bank officials.

Step-by-step explanation:

The 95 percent confidence interval for the mean bad debt ratio for all banks in the Midwest region is (67.02, 68.98). This means that we can be 95 percent confident that the true mean bad debt ratio falls within this range. If the mean bad debt ratio for all Ohio banks is higher than 3.5 percent, which is the mean bad debt ratio for all banks in the Midwest region, then the claim made by the bank officials is likely to be true.

Using the 99 percent confidence interval, which is wider than the 95 percent confidence interval, does not provide more certainty that the claim is true. It only means that we can be 99 percent confident that the true mean bad debt ratio falls within a wider range, which is (67.18, 68.82).