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In: Statistics and Probability

32. Mortgage rates: Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage...

32.

Mortgage rates: 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.

4.750

4.375

4.176

4.679

4.426

4.227

4.125

4.250

3.950

4.191

4.299

4.415

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.

Please show your work.

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