Question

A machine produces metal rods with an average length of 100 cm. A quality control carried out on one of 80 stems allowed to calculate an average length of 99.5 cm and a standard deviation of 1 cm. We want to establish whether the machine needs to be adjusted: with a significance level of 2%, we do a hypothesis test to determine whether the length of the rods produced by the machine is different from 100 cm.

a) State the hypotheses to be tested.

b) What is the decision rule using the critical value (s)? Graphically illustrate the rejection area

c) What decision do you make? Does the machine need to be adjusted?

Answer 1

Solution-A:

Ho;Mu=100

Ha:Mu not =100

Solution-b;

alpha=2%=0.02

df=n-1=80-1=79

t critical in Excel

=T.INV.2T(0.02,79)

=+-2.374481597

Solution-c:

test statistic

t=xbar-mu/s/qrt(n)

=(99.5-100)/(1/sqrt(80))

t=-4.472136

test statisitc is less than t critical

-4.472136<-2.374

Reject Ho

Conclusion:

There is suffcient statistical evidence at 5% level of significance to conclude that the length of the rods produced by the machine is different from 100 cm.

Yes,the machine need to be adjusted as rod length deviates from 100