SOLUTION: 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 reasonabl

Question 1176712: 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
Source: www.bankrate.com
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.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
mean is 4.322 %
sd is 0.226%
99% half CI is t (0.995, df=11)*s/sqrt(n)
=3.106*0.226/sqrt(12)
=0.203
the 99% interval is (4.119, 4.525) units %
-
Because 4.050% is outside the interval, it is reasonable to claim the true rate has risen. We are 99% confident that the true value, whatever it is, lies within the interval.
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