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:

Economic Growth

is the increase in the inflation-adjusted market value of the goods and services produced by an economy over time.

19th Century

the period from January 1, 1801, to December 31, 1900, marked by significant industrial, social, and political changes worldwide.

GNI Per Capita

Gross National Income per capita is a measure dividing the country's GNI by its population, providing an average economic income per person.

Purchasing Power

The quantity and quality of goods and services that can be bought with a unit of currency.