Please explain all steps. Suppose that a researcher, using wage data on 265 rano
ID: 3361332 • Letter: P
Question
Please explain all steps.
Suppose that a researcher, using wage data on 265 ranomly selected male workers and 297 female workers, estimates the OLS regression Wage-13.271+2.247x Male, R-0.07, SER-4.5 (0.2438) (0.3816) 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 What is the estimated gender gap? The estimatod gender gap equals Sper hour.(Round your rosponse to throe decimal places.) The null and alternative hypotheses are H0:A-Oversus H: 40, The +-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 is(Round your response to four decimal places.) The estimated effect of gender gap is statistically significant at the: 1, 5% level 11, 1% level lll. 0.01% level OA. Ill only. B. Iand lI OC.I, II, and IlI D. l only. Construct a 95% confidence interval for the gender gap. The 95% confidence nterval for the effect of Sme r Class on test score is D Round your sponses to two decimal places. From the sample, the average wage of women is Sper hour. (Round your response to three decimal places.)Explanation / Answer
The OLS regression of wage for 265 male and 297 female randomly selcted workers is written below:
Wage_hat = 13.271 + 2.247 * Male, R^2 = 0.07, SER = 4.5
(0.2438) (0.3816)
Male variable is binary and is identify by 1, abd female it is 0. The wage gender gap is the differnce between male and female earnings. From this regression, it is known that the coefficients and their standard errors are as follows:
Beta1_hat = 2.247
Beta0_hat = 13.271
SE (Beta1_hat) = 0.3816
SE (Beta0_hat) = 0.2438
Thus, the estimated gender gap equals $2.247 per hours.
The t-est for the null hypothesis,
H0 : Beta1 hat = 0 against the alternative H1 : Beta1 hat not equal to 0 is:
t = Beta1 hat / SE (Beta1 hat)
= 2.247 / 0.3816
= 5.8884
Therefore, the t-test for the null hypothesis that there is no gender gap is 5.89.
and the p -value for the test is
p-value = Pr(|Z| > |t|)
= 2Pr(Z > 5.89)
= 0.0000
Therefore, the p-value for testing the null hypothesis that there is no gender gap is 0.0000.
The p-value is less than 0.05, 0.01 and 0.0001, so we can reject the null hypothesis that there is no gender gap at a 5%,1% and 0.01% significance level.
Thus, the estimated effect of gender gap is statistical significant at 5%,1% and 0.01% significance level.
Therefore, the correct answer is option c.
The 95% confidence interval for the gender gap Beta1 is:
{2.247 +/- 1.96 * 0.3816}
that is {1.50 <= Beta1 <= 2.99}
Thus, the 95% confidence interval for the effect of small class on test score is (1.50, 2.99).
From the sample, average wage of women is Beta0 hat = $13.271 per hours.
From the sample, average wage of men is
Beta0 hat + Beta1 hat
= 13.271 + 2.247
= $15.518 per hours
The regression estimates calculated from this regression is:
Wage_hat = 15.518 - 2.247 * Female, R^2 = 0.07, SER = 4.5
Gamma1_hat = 2.247
amma0_hat = 15.518
R^2 = 0.07
SER = 4.5