Ten Samples of Size Four Were Taken from a Process

question 45

Essay

Ten samples of size four were taken from a process, and their weights measured. The sample averages and sample ranges are in the following table. Construct and plot an x-bar and R-chart using this data. Is the process in control?
$$\begin{array} { | l | r | r | } \hline \text { Sample } & \text { Mean } & \text { Range } \\\hline 1 & 20.01 & 0.45 \\\hline 2 & 19.98 & 0.67 \\\hline 3 & 20.25 & 0.30 \\\hline 4 & 19.90 & 0.30 \\\hline 5 & 20.35 & 0.36 \\\hline 6 & 19.23 & 0.49 \\\hline 7 & 20.01 & 0.53 \\\hline 8 & 19.98 & 0.40 \\\hline 9 & 20.56 & 0.95 \\\hline 10 & 19.97 & 0.79 \\\hline\end{array}$$

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Definitions:

Fairness Concerns

Issues or discussions surrounding the equitable treatment, distribution of resources or opportunities, and justice in societal, economic, or individual contexts.

Subjective

Subjective pertains to personal opinions, feelings, or tastes, as opposed to objective facts or universal truths.

Overconfidence Effect

A cognitive bias where an individual's subjective confidence in their judgments is greater than their objective accuracy.

Framing Effects

In prospect theory, changes in people’s decision making caused by new information that alters the context, or “frame of reference,” that they use to judge whether options are viewed as gains or losses relative to the status quo.