Suppose You Are a Human Resources Manager at a Large

question 19

Essay

Suppose you are a human resources manager at a large corporation and that you are interested in determining whether a specific training program increases worker productivity (as measured by the number of TPS reports completed)enough to justify its implementation.In an effort to test your theory,you collect data on 672 workers,284 who participated in the training program and 388 who did not,with the dependent variable being measured worker productivity and independent variables being HOURS WORKED,and whether the individual PARTICIPATED in the training program (PARTICIPATED = 1 if the worker participated and 0 if they didn't).Suppose that you estimate the sample regression function (standard errors in parentheses) $$\begin{array} { llll } \text { TPS } { \ \widehat {Rep}orts _{ i } } \text { Hours } _ { i } =& 8.32 + &1.47 \text { Hours Worked } _ { i } +& 2.92 \text { Participated } _ { i } \\&( 1.36 ) & ( 0.68 )&(1.39) \\\end{array}$$
a)How should you interpret the estimated coefficient for PARTICIPATED? Draw a graph and explain.
b)Comment on the statistical significance of the coefficients.
c)How would you change the regression model to account for the possibility that the marginal effect of HOURS WORKED differs for those who participated in the training program and those who don't.Write down the model and explain how to interpret the slope coefficients.
d)How would the coefficient estimates change if you coded PARTICIPATED as 0 and DON'T PARTICIPATE as a 1?

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Definitions:

Wilcoxon Signed Rank Test

A statistical test without assumption of underlying data distribution, designed to evaluate differences in the mean ranks of two paired samples, matched observations, or repeated measures within the same sample to determine variations in their population means.

Normal Approximation

A method used to approximate the distribution of a sum of independent random variables using the normal distribution, under certain conditions.

Continuity Correction

An adjustment made when approximating a discrete distribution with a continuous one, particularly relevant when making inferences about binomial distribution using normal approximation.

Null Hypothesis

A statement in statistics that suggests there is no significant difference or relationship between specified populations, any observed difference being due to sampling or experimental error.