A Quality Analyst Wants to Construct a Sample Mean Chart

question 86

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 in 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: $$\begin{array} { l l c c c } \text { Day } & &{ \text { Weight (ounces) } } \\\hline \text { Monday } & 23 & 22 & 23 & 24 \\\text { Tuesday } & 23 & 21 & 19 & 21 \\\text { Wednesday } & 20 & 19 & 20 & 21 \\\text { Thursday } & 18 & 19 & 20 & 19 \\\text { Friday } & 18 & 20 & 22 & 20\end{array}$$
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

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Definitions:

P-value Approach

A method in statistical hypothesis testing that determines the smallest level of significance at which the null hypothesis can be rejected, based on the observed data.

Null Hypothesis

A statement of no effect or no difference, used as a starting point for statistical hypothesis testing.

Mean Sodium

The average amount of sodium (typically in milligrams) found in a particular sample or set of food items or dietary intake measurements.

Canned Turkey

Processed turkey meat that is preserved in a can for extended shelf life and convenience.