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

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:

$\begin{array}{rrrrrrrr}\hline&&&\text { Actual}&\text {Predict } &&\text { Lower 95\% CL}&\text { Upper 95\% CL }\\\text { OBS } & \text { X1 } & \text { X2 } & \text { Value } & \text { Value } & \text { Residual } & \text { Predict } & \text { Predict } \\1 & 7781 & 644 & 74.707 & 83.175 & -8.468 & 47.224 & 119.126\\\hline \end{array}$ Interpret the 95% prediction interval for y shown on the printout.

A) We are 95% confident that between 47.224 and 119.126 man-hours will be worked during a single day in which 7,781 pieces of mail are processed and 644 checks are cashed.
B) We expect to predict number of man-hours worked per day to within an amount between 47.224 and 119.126 of the true value.
C) We are 95% confident that the number of man-hours worked per day falls between 47.224 and 119.126.
D) We are 95% confident that the mean number of man-hours worked per day falls between 47.224 and 119.126 for all days in which 7,781 pieces of mail are processed and 644 checks are cashed.