Question

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 ( x ₁) and the number of checks cashed per day ( x ₂). Data collected for  n = 20 working days were used to fit the model:

E(y) = β0 + β1x1 + β2x2

A printout for the analysis follows:
_____________________________________________________________________

Analysis of Variance

SOURCE DF SS MS F VALUE PROB>F 13.267 0.0003 MODEL ERROR C TOTAL 2 17 19 7089.06512 4541.72142 11630.78654 3544.53256 267.16008

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 ( x ₁) and the number of checks cashed per day ( x ₂). Data collected for  n = 20 working days were used to fit the model:

E(y) = β0 + β1x1 + β2x2

A printout for the analysis follows:
_____________________________________________________________________

Analysis of Variance

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  α = .05.

Answer 1

From the table of coefficients analysis, we see that there is a t test done for the following set of hypothesis here:

$H_0: \beta_2 = 0$

$H_a: \beta_2 \neq 0$

But as we are testing here whether there is a positive relationship between the dependent variable and the number of checks cashed per day,  x ₂, therefore this is a one tailed test for which the hypothesis here are given as:

$H_0: \beta_2 = 0$

$H_a: \beta_2 > 0$

For the two tailed test, the p-value is given to be 0.0857 as seen from the table. Therefore the p-value for the one tailed test would be computed here as:
= 0.0857/2 = 0.04285

As the p-value here is 0.04285 < 0.05 which is the level of significance, therefore the one tailed test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here for a positive linear relationship between the number of man-hours worked,  y, and the number of checks cashed per day,  x ₂.