Question 366170: A vinyl siding company claims that the mean time to install siding on a medium-size house is at most 20 hours with a standard deviation of 3.7 hours. A random sample of 40 houses sided in the last three years has a mean installation time of 20.8 hours. At the 0.05 significance level, can a claim be made that it takes longer on average than 20 hours to side a house?
a. State the null and alternate hypotheses.
H0: __________________________________________________________________
H1: __________________________________________________________________
b. State the decision rule.
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c. Compute the value of the test statistic.
d. Formulate the decision rule.
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e. What is your decision regarding the null hypothesis? Interpret the result.
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Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A vinyl siding company claims that the mean time to install siding on a medium-size house is at most 20 hours with a standard deviation of 3.7 hours. A random sample of 40 houses sided in the last three years has a mean installation time of 20.8 hours. At the 0.05 significance level, can a claim be made that it takes longer on average than 20 hours to side a house?
a. State the null and alternate hypotheses.
H0: u <= 20
H1: u > 20
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b. State the decision rule.
Reject Ho if the p-value < 5%
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c. Compute the value of the test statistic.
t(20.8) = (20.8-20)/[3.7/sqrt(20)] = 0.9669
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d. Formulate the decision rule.
p9value = P(t >0.9669 when df=19) = 0.1728
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e. What is your decision regarding the null hypothesis? Interpret the result.
Since the p-value is > 5%, fail to reject Ho.
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Cheers,
Stan H.
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