Ten Samples of N = 5 Were Collected to Construct $\overline { x ^ { * } }$

question 49

Multiple Choice

Ten samples of n = 5 were collected to construct an $\overline { x ^ { * } }$ chart. The sample mean and range for each sample are shown in the table below. $$\begin{array} { | c c c | c c c | } \hline \text { Sample } & \text { Mean } & \text { Range } & \text { Sample } & \text { Mean } & \text { Range } \\\hline 1 & 215 & 15 & 6 & 224 & 21 \\2 & 204 & 20 & 7 & 205 & 27 \\3 & 160 & 10 & 8 & 184 & 12 \\4 & 226 & 19 & 9 & 207 & 16 \\5 & 232 & 24 & 10 & 212 & 17 \\\hline\end{array}$$ Calculate the empirical lower and upper control limits for the $\overline { x ^ { * } }$ chart. (You will need a table of control chart factors.) $$\begin{array} { c l l r } \hline \text { Subgroup Size } & d _ { 2 } & D _ { 3 } & D _ { 4 } \\\hline 2 & 1.128 & 0 & 3.267 \\3 & 1.693 & 0 & 2.574 \\4 & 2.059 & 0 & 2.282 \\5 & 2.326 & 0 & 2.114 \\6 & 2.534 & 0 & 2.004 \\7 & 2.704 & 0.076 & 1.924 \\8 & 2.847 & 0.136 & 1.864 \\9 & 2.970 & 0.184 & 1.816 \\\hline\end{array}$$

• A)196.46, 217.34
• B)171.81, 241.39
• C)188.03, 225.17
• D)163.64, 250.56

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Definitions:

Habituation

A decrease in behavioral response after lengthy or repeated exposure to a stimulus.

Conditioning

A process of behavior modification in which a response becomes more frequent or more predictable in a given environment due to reinforcement.

Sensitization

The process whereby a repeated administration of a stimulus results in the progressive amplification of a response.

Operant Conditioning

An educational method where the intensity of an action is altered through either rewards or penalties.