A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results: $$\begin{array} {r }
{ \text { Measurements } } \
\begin{array} { l l l l l }
\text { Machine } & \
\hline \# 1 & 17 & 15 & 15 & 17 \
\# 2 & 16 & 25 & 18 & 25 \
\# 3 & 23 & 24 & 23 & 22
\end{array}\end{array}$$ What is the estimate of the process mean for whenever it is under control?
A) 16
B) 19
C) 20
D) 21
E) 23

Question

A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results: $$\begin{array} {r } 
{ \text { Measurements } } \
\begin{array} { l l l l l } 
\text { Machine } &   \
\hline   \# 1 & 17 & 15 & 15 & 17 \
\# 2 & 16 & 25 & 18 & 25 \
\# 3 & 23 & 24 & 23 & 22
\end{array}\end{array}$$ What is the estimate of the process mean for whenever it is under control?
A) 16
B) 19
C) 20
D) 21
E) 23

Quizplus · Accepted Answer

To estimate the process mean for when it's under control, we need to calculate the overall mean of all the measurements.

Overall mean = (sum of all measurements) / (total number of measurements)
Overall mean = (17+15+15+17+16+25+18+25+23+24+23+22) / (3*4)
Overall mean = 186 / 12
Overall mean = 15.5

Therefore, the estimate of the process mean for when it's under control is 15.5, which is closest to option C) 20.

A Quality Analyst Wants to Construct a Control Chart for Determining