Question

The diameters of steel shafts produced by a certain manufacturing process should have a mean diameter of 0.218 inches. The diameter is known to have a standard deviation of = 0.0003 inch. A random sample of 40 shafts has an average diameter of 0.2455 inches.

a/ Test these hypotheses using α= 0.02, α= 0.05, and α= 0.09

b/ Comparing the data above. Does the results of your hypothesis testing change when you changed α? Explain.

Please show your work and explain. Thanks.

Answer 1

Solution-A:

Ho:mu=0.218

Ha:mu not =0.218

alpha=0.02

test statistic

z=xbar-mu/igma/sqrt(n)

z=(0.2455-0.218)/0.0003/sqrt(40)

z=579.7509

P value in excel

we get left tail prob by NORM.DIST

and 1-left tail=right tail

2*right tail

=NORM.DIST(579.7509,0,1,TRUE)

=1-1

=0

=2*0

p=0.000

for alpha=0.02

p=0..000

p<alpha,reject null hypothesis at 2% level of significance

for alpha=0.05

p<alpha

reject null hypothesis at 5% level of significance

for alpha=0.09

p<alpha

reject null hypothesis at 9% level of significance

b/ Comparing the data above. Does the results of your hypothesis testing change when you changed α?

No since p=0.000

p<0.02,0.05,0.09

Reject null hypothesis

Conclusion:

there is no sufficient statistical evidence at 2%,5% and 9% level of significance to conclude that

The diameters of steel shafts produced by a certain manufacturing process should have a mean diameter of 0.218 inches