Operations Managers Often Use Work Sampling to Estimate How Much $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$

Essay

Operations managers often use work sampling to estimate how much time workers spend
on each operation. Work sampling-which involves observing workers at random points
in time-was applied to the staff of the catalog sales department of a clothing
manufacturer. The department applied regression to data collected for 40 randomly
selected working days. The simple linear model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$ was fit to the data. The printouts for the analysis are given below:
TIME: $\quad y =$ Time spent (in hours) taking telephone orders during the day
ORDERS: $\quad x =$ Number of telephone orders received during the day
UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME
$\begin{array}{l}\text { PREDICTOR }\\\begin{array}{l|c|c|c|c}\text { PREDICTOR } & & & & \\\text { VARIABLES } & \text { COEFFICIENT } & \text { STD ERROR } & \text { STUDENT'ST } & \mathrm{P} \\\hline \text { CONSTANT } & 10.1639 & 1.77844 & 5.72 & 0.0000 \\\text { ORDERS } & 0.05836 & 0.00586 & 9.96 & 0.0000\end{array}\end{array}$

$\begin{array}{lclc}\text { R-SQUARED } & 0.7229 & \text { RESID. MEAN SQUARE (MSE) } & 11.6175 \\\text { ADJUSTED R-SQUARED } & 0.7156 & \text { STANDARD DEVIATION } & 3.40844\end{array}$


$\begin{array}{l|r|c|c|c|c}\text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & \mathrm{F} & \mathrm{P} \\\hline \text { REGRESSION } & 1 & 1151.55 & 1151.55 & 99.12 & 0.0000 \\\text { RESIDUAL } & 38 & 441.464 & 11.6175 & & \\\text { TOTAL } & 39 & 1593.01 & & &\end{array}$

CASES INCLUDED 40 MISSING CASES 0
Conduct a test of hypothesis to determine if time spent (in hours) taking telephone orders during the day and the number of telephone orders received during the day are positively linearly related. Use $\alpha = .01$ .