Suppose that a researcher, using wage data on 250 randomly selected male workers and 280 female workers, estimates the OLS regression Wage 12.52 + 2.12 X Male, R2= 0.06, SER = 4.2, %3D (0.23) (0.36) where Wage is measured in dollars per hour and Male is a binary variable that is equal to 1 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 gåp? b. Is the estimated gender gap significantly different from 0? p-value for testing the null hypothesis that there is no gender gap.) te the c. Construct a 95% confidence interval for the gender gap. d. In the sample, what is the mean wage of women? Of men?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 6EA
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Suppose that a researcher, using wage data on 250 randomly selected male
workers and 280 female workers, estimates the OLS regression
Wage
= 12.52 + 2.12 X Male, R2 0.06, SER = 4.2,
(0.23) (0.36)
where Wage is measured in dollars per hour and Male is a binary variable
that is equal to 1 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 gåp?
b. Is the estimated gender gap significantly different from 0? (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?
Transcribed Image Text:Suppose that a researcher, using wage data on 250 randomly selected male workers and 280 female workers, estimates the OLS regression Wage = 12.52 + 2.12 X Male, R2 0.06, SER = 4.2, (0.23) (0.36) where Wage is measured in dollars per hour and Male is a binary variable that is equal to 1 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 gåp? b. Is the estimated gender gap significantly different from 0? (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?
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