Some people who bought ABC server systems complained about having received defec
ID: 3065190 • Letter: S
Question
Some people who bought ABC server systems complained about having received defective systems. The industry standard for such systems has been ninety-five percent non-defective systems. In a sample of 82 units sold, 4 units were defective.
Compute the proportion of defective items in the sample.
Compute the standard error of p.
Compute the test statistic for p.
Compute the critical value at 97% confidence
Using the critical value approach, test to see if the percentage of defective systems produced by ABC has exceeded the industry standard.
Show that the p-value approach results in the same conclusion as that of part b.
What is your conclusion? Is ABC significantly better or worse than the industry?
Explanation / Answer
Compute the proportion of defective items in the sample.
=4/82
= 0.048780
Compute the standard error of p.
=sqrt(0.05*0.95/82)
= 0.0240679
Compute the test statistic for p.
TS =( 0.048780 - 0.05 )/0.0240679
= -0.050689
Compute the critical value at 97% confidence
critical value = -1.88
Using the critical value approach, test to see if the percentage of defective systems produced by ABC has exceeded the industry standard.
since -0.050689 > -1.88
we fail to reject the null hypothesis
Show that the p-value approach results in the same conclusion as that of part b.
p-value = P(Z < -0.050689) = 0.52
since p-value > 0.03
we fail to reject the null
What is your conclusion? Is ABC significantly better or worse than the industry
ABC is better than the industry