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

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 $\alpha = .05$ .