A Quality Analyst Wants to Construct a Sample Mean Chart

question 152

Essay

A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that the process standard deviation is two ounces. Each day last week, he randomly selected four packages and weighed each. The data from that activity appears below. $$\begin{array} { | l | l | l | l | l | } \hline & { \text { Weight } } \\\hline \text { Day } & \text { Package } 1 & \text { Package } 2 & \text { Package 3 } & \text { Package 4 } \\\hline \text { Monday } & 23 & 22 & 23 & 24 \\\hline \text { Tuesday } & 23 & 21 & 19 & 21 \\\hline \text { Wednesday } & 20 & 19 & 20 & 21 \\\hline \text { Thursday } & 18 & 19 & 20 & 19 \\\hline \text { Friday } & 18 & 20 & 22 & 20 \\\hline\end{array}$$ (a) Calculate all sample means and the mean of all sample means.
(b) Calculate upper and lower control limits that allow for natural variations.
(c) Is this process in control?

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Definitions:

Quantity Demanded

The total amount of a good or service that consumers are willing and able to purchase at a given price level in a market.

Quantity Supplied

The quantity of a product or service suppliers are prepared to offer for sale at a specific price.

Price Ceiling

A government-imposed limit on how high a price can be charged on a product, aiming to keep essential goods affordable.

Quantity Demanded

The total amount of a good or service that consumers are willing to purchase at a given price over a specified period.