A Quality Analyst Wants to Construct a Sample Mean Chart

question 50

Multiple Choice

A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is under control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each: $$\begin{array} { r } { \text { Weight (ounces) } }\\\begin{array} { l l l l l } \text { Day } \\\hline \text { Monday } & 23 & 22 & 23 & 24 \\\text { Tuesday } & 23 & 21 & 19 & 21 \\\text { Wednesday } & 20 & 19 & 20 & 21 \\\text { Thursday } & 18 & 19 & 20 & 19 \\\text { Friday } & 18 & 20 & 22 & 20\end{array}\end{array}$$ If he uses upper and lower control limits of 22 and 18 ounces, what is his risk (alpha) of concluding this process is out of control when it is actually in control (Type I error) ?

• A) 0.0026
• B) 0.0456
• C) 0.3174
• D) 0.6826
• E) 0.9544

---

Definitions:

Control Theories

Theories in criminology and sociology that explain social order and the lack of criminal behavior as a result of societal norms and relationships that encourage conformity.

Deviance

Behavior or actions that violate societal norms or expectations, often leading to social disapproval or sanctions.

Crime

Crime is an act or omission that violates the law and is punishable by the state or other authority.

Compelling Explanation

A persuasive and cogent reason or argument that effectively explains a phenomenon, idea, or event.