In Any Production Process in Which One or More Workers $( y )$

question 108

Essay

In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked $( y )$ per day by the clerical staff depends on the number of pieces of mail processed per day $\left( x _ { 1 } \right)$ and the number of checks cashed per day $\left( x _ { 2 } \right)$ . Data collected for $n = 20$ working days were used to fit the model:
$$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$$
A partial printout for the analysis follows:

$\begin{array}{l}\text { Analysis of Variance }\\\begin{array}{lrrrrr}\text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & \text { F VALUE } & \text { PROB > F } \\\text { MODEL } & 2 & 7089.06512 & 3544.53256 & 13.267 & 0.0003 \\\text { ERROR } & 17 & 4541.72142 & 267.16008 & & \\\text { C TOTAL } & 19 & 11630.78654 & & &\end{array}\end{array}$

$\begin{array}{llll}\text { ROOT MSE } & 16.34503 & \text { R-SQUARE } & 0.6095 \\\text { DEP MEAN } & 93.92682 & \text { ADJ R-SQ } & 0.5636 \\\text { C.V. } & 17.40188 & &\end{array}$


Test to determine if the model is adequate for predicting the number of man-hours worked. Use $\alpha = .025$ .

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Definitions:

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Units of time, typically consisting of 28 to 31 days, used in calendars to divide the year into twelve periods.