The chair of the operations management department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are in control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results: $$\begin{array} { l c }
\text { Instructor } & \text { Number of Failures } \
\hline \text { Prof. A } & 13 \
\text { Prof. B } & 0 \
\text { Prof. C } & 11 \
\text { Prof. D } & 16
\end{array}$$
What are the .95 (5 percent risk of Type I error) upper and lower control limits for the p-chart?
A) .95 and .05
B) .13 and .07
C) .1588 and .0412
D) .16 and .04
E) .1774 and .0226

Question

The chair of the operations management department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are in control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results: $$\begin{array} { l c } 
\text { Instructor } & \text { Number of Failures } \
\hline \text { Prof. A } & 13 \
\text { Prof. B } & 0 \
\text { Prof. C } & 11 \
\text { Prof. D } & 16
\end{array}$$
What are the .95 (5 percent risk of Type I error) upper and lower control limits for the p-chart?
A) .95 and .05
B) .13 and .07
C) .1588 and .0412
D) .16 and .04
E) .1774 and .0226

Quizplus · Accepted Answer

To construct a p-chart, we need to first determine the overall sample proportion of failures ($\hat{p}$):
$$\hat{p}=\frac{	ext{Total number of failures}}{	ext{Total sample size}}=\frac{13+0+11+16}{100+100+100+100}=0.1$$

Next, we can calculate the standard deviation of the sample proportion ($\sigma_{\hat{p}}$) using the following formula:
$$\sigma_{\hat{p}}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\sqrt{\frac{0.1(0.9)}{100}}=0.03$$

Now, we can calculate the upper and lower control limits:
$$	ext{UCL}=\hat{p}+3\sigma_{\hat{p}}=0.1+3(0.03)=0.19$$
$$	ext{LCL}=\hat{p}-3\sigma_{\hat{p}}=0.1-3(0.03)=0.01$$

Therefore, the .95 upper and lower control limits for the p-chart are 0.19 and 0.01, respectively. The best choice is (C).

The Chair of the Operations Management Department at Quality University