Suppose that a researcher, using wage data on 250 randomly selected male workers

Question

Suppose that a researcher, using wage data on 250 randomly selected male workers and 280 female workers, estimates the OLS regression, 4.2 Wage = 12.68 + 2.79 Male, R-= 0.06, SER-3.10 (0.18) (0.84) where Wage is measured in S/hour and Male is a binary variable that is equal to one if the person is a male and 0 if the person is a female. Define the wage gender gap as the difference in mean earnings between men and women. a. What is the estimated gender gap? b. Is the estimated gender gap significantly different from zero? (Compute the p-value for testing the null hypothesis that there is no gender gap.) c. Construct a 95% confidence interval for the gender gap. d. In the sample, what is the mean wage of women? Of men? e. Another researcher uses these same data, but regresses Wages on Female, a variable that is equal to one if the person is female and zero if the person a male. What are the regression estimates calculated from this regression? wage = Felliale, R? SER =

Explanation / Answer

a) The estiamted gender gap = 2.79

b)
H0: gender gap significantly not different from zero
H1: gender gap significantly different from zero
Test statsitic
t = 2.79/0.84 = 3.32143

P-value = 0.000
Here P-value < alpha 0.05, we reject H0
thus we conclude that gender gap significantly different from zero

c) The 95% confidence interval of the gender gap is
Gender gap +/- t critical value * SE = 2.79 +/- 1.96*0.84 =(1.1436,4.4364)

d) The mean wage of women is 12.68+2.79(0) = 12.68
The mean wage of men is 12.68+2.79(1) = 15.47  

e) Wage = 12.68 - 2.79 Female, R^2= 0.06, SER = 3.10

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.