Question

A vinyl siding company claims that the mean time to install siding on a medium-size house is at most 20 hours. Assume the populatin standard deviation is 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 alternative hypothesis.

b. Formulate the rejection rule.

c. Do you reject the null hypothesis?

d. Can you conclude that it takes longer than the advertised 20 hours to side a house?

Answer 1

P-value = 0.086

c]

Decision rule: 1) If p-value <= level of significance (alpha) then we reject null hypothesis

                      2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.086 > 0.05 so we used 2nd rule.

That is we fail to reject null hypothesis

We do not reject null hypothesis at 5% level of significance, because P-value > \alpha = 0.05

d]

Conclusion: At 5% level of significance there is insufficient evidence to say that the mean installation time is longer than 20 hrs.