Twenty-Five Samples of Size 4 Were Drawn from a Production

Essay

Twenty-five samples of size 4 were drawn from a production process. For each sample, the mean and range were computed as shown below.
$$\begin{array}{l}\begin{array} { | c | c c c c c c c c c c c c c | } \hline \text { Sample } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 \\\hline \bar { x } _ { j } & 21 & 24 & 20 & 18 & 20 & 21 & 23 & 25 & 15 & 20 & 25 & 21 & 4 \\R _ { j } & 8 & 12 & 7 & 19 & 6 & 11 & 8 & 8 & 7 & 13 & 9 & 13 & 25 \\\hline\end{array}\\\\\begin{array} { | c | c c c c c c c c c c c c | } \hline \text { Sample } & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 & 25 \\\hline \bar { x } _ { j . } & 28 & 14 & 22 & 24 & 26 & 19 & 14 & 28 & 17 & 26 & 29 & 15 \\R _ { j } & 12 & 14 & 17 & 8 & 21 & 12 & 14 & 11 & 7 & 15 & 21 & 19 \\\hline\end{array}\end{array}$$
-Does it appear that the process is under control? Explain.