In Any Production Process in Which One or More Workers $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$$

question 87

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 (x1) and the number of checks cashed per day (x2). 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:

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

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


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

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Definitions:

Contraction

The process of a muscle becoming shorter and tighter, usually in response to a nerve impulse.

Isometric Contraction

Muscle contraction in which the length of the muscle does not change but the tension produced increases.

Action Potential

A temporary reversal of the electrical potential across the membrane of a nerve cell (neuron) that occurs when the cell generates a nerve impulse.

Muscle Fibers

The cells that make up skeletal muscles, capable of contracting to produce movement and force.