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

question 126

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 printout for the analysis follows:
$\begin{array}{lrrrrr}\hline & {\text { Analysis of Variance }} \\& & & & \\\text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & \text { F VALUE } & \text { PROB > F } \\& 2 & 7089.06512 & 3544.53256 & 13.267 & 0.0003 \\\text { MODEL } & 17 & 4541.72142 & 267.16008 & & \\\text { ERROR } & 19 & 11630.78654 & & &\end{array}$

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

$\begin{array}{lrrrrr} & \text { PARAMETER } & \text { STANDARD } & \text { T FOR 0: } & \\\text { VARIABLE } & \text { DF } & \text { ESTIMATE } & \text { ERROR } & \text { PARAMETER }=0 & \text { PROB }>|\mathrm{T}| \\\text { INTERCEPT } & 1 & 114.420972 & 18.68485744 & & \\\text { X1 } & 1 & -0.007102 & 0.00171375 & 6.124 & 0.0001 \\\text { X2 } & 1 & 0.037290 & 0.02043937 & -4.144 & 0.0007 \\& & 1.824 & 0.0857\end{array}$

$\begin{array}{rrrrrrrr}\text { OBS } & \text { X1 } & \text { X2 } & \begin{array}{r}\text { Actual } \\\text { Value }\end{array} & \begin{array}{r}\text { Predict } \\\text { Value }\end{array} & \text { Residual } & \begin{array}{r}\text { Lower 95\% CL } \\\text { Predict }\end{array} & \begin{array}{r}\text { Upper 95\% CL } \\\text { Predict }\end{array} \\\hline & 7781 & 644 & 74.707 & 83.175 & -8.468 & 47.224 & 119.126 \\\hline\end{array}$

Test to determine if there is a positive linear relationship between the number of man-hours worked, $y$ , and the number of checks cashed per day, $x _ { 2 }$ . Use $\alpha = .05$ .

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Definitions:

Confidence Interval Estimate

A range of values derived from sample statistics that is likely to contain the value of an unknown population parameter, with a specified level of confidence.

Average Age

The mean age of a group of individuals, calculated by summing their ages and dividing by the number of individuals.

Male Employees

Refers to workers or staff members within an organization who are identified as male.

Female Employees

The segment of the workforce that identifies as female, often analyzed in studies regarding workplace diversity and equality.