A quality analyst wants to construct a control chart for determining whether four machines, all producing the same product, are in control with regard to a particular quality attribute. Accordingly, she inspected 1,000 units of output from each machine in random samples, with the following results: $$\begin{array} { c c }
\text { Machine } & \text { Total Defectives } \
\hline \# 1 & 23 \
\# 2 & 15 \
\# 3 & 29 \
\# 4 & 13
\end{array}$$
What is the estimate of the standard deviation of the sampling distribution of sample proportions for this process?
A) .016
B) .00016
C) .04
D) .0044
E) .00002

Question

A quality analyst wants to construct a control chart for determining whether four machines, all producing the same product, are in control with regard to a particular quality attribute. Accordingly, she inspected 1,000 units of output from each machine in random samples, with the following results: $$\begin{array} { c c } 
\text { Machine } & \text { Total Defectives } \
\hline \# 1 & 23 \
\# 2 & 15 \
\# 3 & 29 \
\# 4 & 13
\end{array}$$
What is the estimate of the standard deviation of the sampling distribution of sample proportions for this process?
A) .016
B) .00016
C) .04
D) .0044
E) .00002

Quizplus · Accepted Answer

The standard deviation of the sampling distribution of sample proportions is calculated using the formula: $\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the overall proportion of defectives and $n$ is the sample size. Here, $p = \frac{23+15+29+13}{4000} = \frac{80}{4000} = 0.02$ and $n = 1000$. Thus, the standard deviation is $\sqrt{\frac{0.02(1-0.02)}{1000}} = 0.0044$.

A Quality Analyst Wants to Construct a Control Chart for Determining