Question

You run your printer 1000 times and find that your 3D printer fails 1 every 50 prints. The manufacturer claims that the printer will only fail 1% of the time.

a Create a confidence interval for the failure rate of your printer.

b Is the failure rate of your printer different than that of the manufactures? Make sure to include the null and alternative hypothesis, z score, p value and interpretation of the results.

c Is the failure rate of your printer greater than that of the manufactures? Make sure to include the null and alternative hypothesis, z score, p value and interpretation of the results.

Answer 1

Solution-A:

p^=x/n=50/1000=0.05

z crit for 95%=1.96

95% confidence interval  for the failure rate of your printer.

p^-z*sqrt(p^*(1-p^)/n),p^+z*sqrt(p^*(1-p^)/n)

0.05-1.96*sqrt(0.05*(1-0.05/1000),0.05+1.96*sqrt(0.05*(1-0.05/1000)

0.03649163, 0.06350837

3.649163,6.350837

Solution-b:

Ho:p=0.01

Ha:p not =0.01

alpha=0.05

z=p^-p/sqrt(p*(1-p)/n)

=(0.05-0.01)/sqrt(0.01*(1-0.01)/1000)

z=12.71283

test statistic,z=12.71283

p value in excel

=2*(=NORM.S.DIST(-12.71283,TRUE))

=5.01848E-37

P=0.000

p<0.05

Reject Ho

Accept Ha

Conclusion:There is sufficient statistical evidence at 5% level of significance to support the claim that

failure rate of your printer different than that of the manufactures

Solution-c:

Ho:p=0.01

Ha:p>0.01

alpha=0.05

z=p^-p/sqrt(p*(1-p)/n)

=(0.05-0.01)/sqrt(0.01*(1-0.01)/1000)

z=12.71283

p value right tail

==NORM.S.DIST(-12.71283,TRUE)

2.50924E-37

p=0.0000

p<0.05

Reject Ho
Accept Ha

Conclusion:

There is sufficient statistical evidence at 5% level of significance to conclude that failure rate of your printer greater than that of the manufactures