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 partial printout for the analysis follows:


Interpret the $95 \%$ prediction interval for $y$ shown on the printout.

A) 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.
B) 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.

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 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.