SOLUTION: A recent article in The Wall Street Journal reported that the 30-year mortgage rate is now less than 6 percent. A sample of eight small banks in the Midwest revealed the followin

Question 1162777: A recent article in The Wall Street Journal reported that the 30-year mortgage rate is
now less than 6 percent. A sample of eight small banks in the Midwest revealed the
following 30-year rates (in percent):
4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6
At the .01 significance level, can we conclude that the 30-year mortgage rate for small
banks is less than 6 percent? Estimate the p-value.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Mean is 5.6375%
s=0.6345
Ho: rate is >=6%
Ha: rate < 6%
assuming that the distribution is normal or very close to it, and s is a decent estimator of sigma, use a t-test
where the test statistic is t=(x bar-mean)/s/sqrt(8)
with
critical value is t<-2.998 with t(0.99, df=7)
t=-0.3625*sqrt(8)/0.6345
=-1.616
There is insufficient evidence to reject Ho at the 1% level
estimate p at about 0.06 (5% z would be -1.645, and this is less than that.
It is actually 0.075

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