A vinyl sidingcompany claims that the mean time to install siding on amedium-siz

Question

A vinyl sidingcompany claims that the mean time to install siding on amedium-size house is at most 20 hours with a standard deviation of3.7 hours. A random sample of 40 houses sided in the last threeyears has a mean installation time of 20.8 hours. At the 0.05significance level, can a claim be made that it takes longer onaverage than 20 hours to side a house?

        a.   State the null and alternatehypotheses.

              H0:____________________________________________________________________

              H1:____________________________________________________________________

b.      State the valueof alpha. _______________

c.       State thetest statistic that you will use and why. _______________

d.      State thedecision rule. _______________

e.       Compute theobserved value of the test statistic and state your conclusion.

Explanation / Answer

  =20, =3.7

  n=40, X-bar=20.8

  =0.05

     a.   State thenull and alternate hypotheses.

              H0: __<=20__________________________________________________________________

              H1: __>20__________________________________________________________________

b.      State the valueof alpha. _=0.05______________

c.       State thetest statistic that you will use and why. __

          Z=(X-bar-)/(/n)=(20.8-20)/(3.7/40)=1.367_____________

d.      State thedecision rule. Z>Z0.05=1.645______________

e.       Compute theobserved value of the test statistic and state yourconclusion.

         Since X=1.367<1.645, do not reject Ho.

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