Suppose the following table was generated from the sample data of 20 employees r

Question

Suppose the following table was generated from the sample data of 20 employees relating annual salary to years of education and gender. According to the results, is there a salary difference between men and women at the 0.01 level of significance? If yes, write the difference in salary in the space provided, rounded to two decimal places. Else, select "There is not enough evidence" Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used. _____

Explanation / Answer

The p value corresponding to gender for t(4.04) is 0.000844. Per rejection rule based on p value, reject null hypothesis [H0: beta2=0 (gender is not an useful predictor of annual salary of employees)] if p value is less than alpha=0.01. Here, p value is less than 0.01, therefore, reject null hypothesis and conclude that gender is an useful predictor for estimating annual salary of employees. In other words there is significant salary difference between men and women.

The regression equation for determining annual salary is:

-10982.510308+3781.071481x1+3879.858676x2

Substitute x2 with 1 to obtain annual salary for female and with 0 to obtain annual salary for male.

Thus, annual salary for male is 3781.071481x1-10982.510308 ...(1)

annual salary for female is 3781.071481x1-7102.651632 ...(2)

Subtract 1-2 to obtain the difference in annual salary of male and female.

Difference: $3879.86

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