Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia on a recent day. It is reasonable to assume that the population is approximately normal.

a. Construct a 99% confidence interval for the mean rate.

b. One week earlier, the mean rate was 4.050%. A mortgage broker claims that the mean rate is now higher. Based on the confidence interval, is this a reasonable claim? Explain.

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4.750 4.375 4.176 4.679 4.426 4.227 4.125 4.250 3.950 4.191 4.299 4.415