Question

A researcher has designed the relationship between the salaries of selected employees of an organization (shown as "EARN" in $/hour) and their years of education (shown as "YRSEDUC", in years) and their age (shown as "AGE" in years) and their gender (shown as the binary variable "MALE", which "MALE"=0 indicates a male employee, and "MALE"=0 otherwise) as hereunder. A total number of (i) employees were selected for this study:

EARN(i) = B(0) + B(1) YRSEDUC(i) + B(2) AGE(i) + B(3) MALE(i) + u(i)

Using the above findings, answer the following questions:

A-Comment about the slope coefficient of the variable "MALE"

B-Suppose that the t-ratio of the corresponding slope coefficient for "MALE" becomes -0.58 in an estimated regression. Verify if "MALE" is an important variable in the estimated regression. (Use a 5% level of significance and a two-sided test. Show all required steps)

Answer 1

Answer a: B3 is the slope coefficient for the variable Male which basically shows that given that the ith individual is a male, the expected salary of the selection employee of an organization is on an average B3 $/ hour higher than when compared to others.

Answer b: The null hypothesis, Ho: B3=0

Alternative hypothesis, H1: B3~=0

We need to perform a double tailed t test here and the t calculated value is given as -0.58. Now we know that decision criteria for rejecting or not rejecting a null hypothesis is that:

If |t calculated|> t critical value, then we reject Ho but if |t calculated| < t critical value, then we don't reject Ho. Looking at the t table we find that t critical value is 1.96 which is greater than 0.58. This means that we don't reject the null hypothesis which simply means that " Male" is not an important variable in the estimated regression.