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:
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Analysis of Variance

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ROOT MSE

16.34503

R-SQUARE

0.6095

DEP MEAN  93.92682  ADJ R-SQ  0.5636
C.V.  17.40188

Parameter Estimates

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

The hypothesis being tested is:

H₀: β₂ = 0

H₁: β₂ > 0

The test statistic, t = 1.824.

The p-value is 0.04285.

Since the p-value (0.04285) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a positive linear relationship between the number of man-hours worked,  y, and the number of checks cashed per day,  x ₂.