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1. 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 male ; R^2 = 0.06 ;? = 4.2

and (0.23) (0.36) where the quantity in parentheses is the standard error of the estimated coefficient.
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.
1. What is the estimated gender gap?
2. Is the estimated gender gap significantly different from zero?
3. Construct a 95% confidence interval for the gender gap.
4. In the sample, what is the mean wage of women? Of men?
5. Another researcher uses these same data but regresses wages on female, a variable that
is equal to 1 if the person is female and 0 if the person is a male. What are the regression
estimates calculated from this regression? And the
R2 coefficient?

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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

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Edwin Sinclar, MBA
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  • MBA, Aspen University
  • Bachelor of Science , Berea College
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