Question 401555: 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 stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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Ho: p>= 6
H1: p < 6 (claim)
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p-hat = 5.64
test stat: z(5.64) = (5.64-6)/[0.63/sqrt(8)] = -1.6162..
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p-value: P(z< -1.6162) = 0.0530
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Conclusion:
Since the p-value is greater than 1%, fail to reject Ho.
The test results support the claim at the 1% level.
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Cheers,
Stan H.
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