Some people who bought ABC server systems complained about having received defec

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

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