Question

Suppose that a researcher, using wage data on 230 randomly selected male workers and 258 fermale workers, estimates the OLS regression 4 Wage 11.518 +1.950 x Male, R 0,04, SER = 3.9, (0.2116) (0.3312) 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 0if the person is a female. Define the wage gender gap as the difference in mean earnings between men and women. What is the estimated gender gap? The estimated gender gap equals $ per hour. (Round your response to three decimal places.) The null and alternative hypotheses are Ho: B, 0 versus H: B, #0. The t-statistic for testing the null hypothesis that there is no gender gap is (Round your response to two decimal places.) The p-value for testing the null hypothesis that there is no gender gap decimal places.) (Round your response to four The estimated effect of gender gap is statistically significant at the: I. 5% level II. 1% level III. 0.01% level O A. I, II, and I. O B. Il only. O C. Ionly. O D. I and Il. Construct a 95% confidence interval for the effect of gender gap. ). (Round your responses to The 95% confidence interval for the effect of gender gap is ( two decimal places.) per hour. (Round your response to three decimal From the sample, the average wage of women is $ places.) per hour. (Round your response to three decimal places.) From the sample, the average wage of men is $ 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 a male. What are the regression estimates calculated from this regression? A A Wage = Yo1 x Female, R, SER (Round your response to three decimal places.) 7, (Round your response to three decimal places.) R = (Round your response to two decimal places.) (Round your response to one decimal place.) SER= +

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Answer 1

4. The given model is:
$\dpi{80} \fn_phv \small \widehat{Wage}=11.518+1.95Male$

a. In this model, the coefficient of the dummy variable iss 1.95. Average wage of females is 11.518. Average wage of males is 13.468. The estimated wage gap between males and females is 1.95.

b. The t statistic is:
$\dpi{80} \fn_phv \small t^{est}=\frac{\hat{\beta_1}-\beta_1^{H_0}}{SE(\hat{\beta_1})}=\frac{1.95-0}{0.3312}=5.88$

c. The p-value corresponding to this t statistic is computed using the t table for 486 degrees of freedom. Since number of degrees of freedom is greater than 30, this value can be estimated using the standard normal distribution. The largest value in the z table is 3.99. p-value corresponding to that value is 0.000015~0.0001.

d. The p-value denotes the maximum probability of type 1 error which is the level of significance. Since this p-value is less than 5%, 1%, and 0.01%, therefore, it is statistically significant under all these levels of confidence.

e. The 95% confidence interval is computed by finding the t-values corresponding to 0.05 level of significance for a one tailed test. Since the number of degrees of freedom is very large, standard normal distribution can be used to estimate this confidence interval. The confidence interval is:
$\dpi{80} \fn_phv \small 1.950\pm1.96*0.3312\rightarrow (-1.3,2.59)$

f. From the sample, average wage of women is the avergae wage when the dummy variable male is equal to 0. This value is 11.518.