Question

Suppose the following table was generated from the sample data of 2020 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 0.010.01 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."

	Coefficients	Standard Error	t Stat	P-Value
Intercept	−6351.081919	2302.895692	−2.757868	0.013444
Education	3487.0714766	133.810154	26.059842	0.000000
Male (1 if male, 0 if female)	2400.745462	794.341077	3.022311	0.007680

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.

Answer 1

Solution:

The p value corresponding to dummy variable representing male and female = 0.007680.

Significance level () = 0.01

Decision:

P- Value <

0.007680 < 0.01

Since the P - value is less than 0.01, So we reject the null hypothesis(H0)and conclude that there is enough evidence of salary difference between men and women.

So there is significant salary difference between men and women.

Therefore, the Regression equation is given by

Salary = −6351.081919 + 3487.071476* Education + 2400.745462 * Female

for Females, value of the variable Female = 1
For Males, value of the variable Female = 0

Therefore Keeping all the other conditions constant, Salary is dependent on the value of the variable Female.

Hence there is a salary difference between men and women  is given by

Salary Difference = 2400.745462(1-0)

Salary Difference = 2400.745462(1)

Salary Difference = 2400.745462

Salary Difference = $2400.75