SOLUTION: 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 s

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.
_______________________________________________________________________
c. Compute the value of the test statistic.

d. Formulate the decision rule.
_______________________________________________________________________
e. What is your decision regarding the null hypothesis? Interpret the result.
_______________________________________________________________________
_______________________________________________________________________

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
------------------------
b. State the decision rule.
Reject Ho if the p-value < 5%
_______________________________________________________________________
c. Compute the value of the test statistic.
t(20.8) = (20.8-20)/[3.7/sqrt(20)] = 0.9669
-------------------------
d. Formulate the decision rule.
p9value = P(t >0.9669 when df=19) = 0.1728
_______________________________________________________________________
e. What is your decision regarding the null hypothesis? Interpret the result.
Since the p-value is > 5%, fail to reject Ho.
-----------------------------
Cheers,
Stan H.
_______________________________________________________________________

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