In any production process in which one or more workers are e

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) = Bo + B1x1+ B2x2

A partial printout for the analysis follows: Predicted

OBS x1 x2 Actual value predicted value Residual lower 95%CL Upper 95% CL   

1 7781 644 74.707 83.175 -8.468 47.224 119.126

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

A)We are 95% confident that the number of man-hours worked per day falls between 47.224 and 119.12.

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 expect to predict number of man-hours worked per day to within an amount between 47.224 and 119.126 of the true value.

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.

Solution

A 95% Confidence Interval implies that one is 95% certain contains the true mean of the population. Hence we can conclude that:

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.