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Suppose that a researcher, using wage data on 258 randomly selected male workers and 288 female workers, estimates the OLS regression Wage= = 12.896 +2.184 × Male, R² = 0.07, SER = 4.3, (0.2369) (0.3708) 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 estimated gender gap equals $ 2.184 per hour. (Round your response to three decimal places.) The null and alternative hypotheses are Ho: B₁ = 0 versus H₁: ³₁ ±0. The t-statistic for testing the null hypothesis that there is no gender gap is 0.51. (Round your response to two decimal places.) The p-value for testing the null hypothesis that there is no gender gap is 0. (Round your response to four decimal places.) The estimated effect of gender gap is statistically significant at the: I. 5% level II. 1% level III. 0.01% level ○ A. I and II. B. I only. C. I, II, and III. D. Ill only. Construct a 95% confidence interval for the effect of gender gap. The 95% confidence interval for the effect of gender gap is ( -6.24 10.61 (Round your responses to two decimal places.) From the sample, the average wage of women is $ per hour. (Round your response to three decimal places.) From the sample, the average wage of men is $ per hour. (Round your response to three decimal places.) 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? Wage = ^ Yo R² = = SER = Λ Yo + 1 ₁ × Female, R², SER. (Round your response to three decimal places.) (Round your response to three decimal places.) (Round your response to two decimal places.) (Round your response to one decimal place.)

Suppose that a researcher, using wage data on 258 randomly selected male workers and 288 female workers, estimates the OLS regression Wage= = 12.896 +2.184 × Male, R² = 0.07, SER = 4.3, (0.2369) (0.3708) 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 estimated gender gap equals $ 2.184 per hour. (Round your response to three decimal places.) The null and alternative hypotheses are Ho: B₁ = 0 versus H₁: ³₁ ±0. The t-statistic for testing the null hypothesis that there is no gender gap is 0.51. (Round your response to two decimal places.) The p-value for testing the null hypothesis that there is no gender gap is 0. (Round your response to four decimal places.) The estimated effect of gender gap is statistically significant at the: I. 5% level II. 1% level III. 0.01% level ○ A. I and II. B. I only. C. I, II, and III. D. Ill only. Construct a 95% confidence interval for the effect of gender gap. The 95% confidence interval for the effect of gender gap is ( -6.24 10.61 (Round your responses to two decimal places.) From the sample, the average wage of women is $ per hour. (Round your response to three decimal places.) From the sample, the average wage of men is $ per hour. (Round your response to three decimal places.) 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? Wage = ^ Yo R² = = SER = Λ Yo + 1 ₁ × Female, R², SER. (Round your response to three decimal places.) (Round your response to three decimal places.) (Round your response to two decimal places.) (Round your response to one decimal place.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 34EQ
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Suppose that a researcher, using wage data on 258 randomly selected male workers and 288 female workers, estimates the OLS regression Wage= = 12.896 +2.184 × Male, R² = 0.07, SER = 4.3, (0.2369) (0.3708) 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 estimated gender gap equals $ 2.184 per hour. (Round your response to three decimal places.) The null and alternative hypotheses are Ho: B₁ = 0 versus H₁: ³₁ ±0. The t-statistic for testing the null hypothesis that there is no gender gap is 0.51. (Round your response to two decimal places.) The p-value for testing the null hypothesis that there is no gender gap is 0. (Round your response to four decimal places.) The estimated effect of gender gap is statistically significant at the: I. 5% level II. 1% level III. 0.01% level ○ A. I and II. B. I only. C. I, II, and III. D. Ill only. Construct a 95% confidence interval for the effect of gender gap. The 95% confidence interval for the effect of gender gap is ( -6.24 10.61 (Round your responses to two decimal places.)
Transcribed Image Text:Suppose that a researcher, using wage data on 258 randomly selected male workers and 288 female workers, estimates the OLS regression Wage= = 12.896 +2.184 × Male, R² = 0.07, SER = 4.3, (0.2369) (0.3708) 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 estimated gender gap equals $ 2.184 per hour. (Round your response to three decimal places.) The null and alternative hypotheses are Ho: B₁ = 0 versus H₁: ³₁ ±0. The t-statistic for testing the null hypothesis that there is no gender gap is 0.51. (Round your response to two decimal places.) The p-value for testing the null hypothesis that there is no gender gap is 0. (Round your response to four decimal places.) The estimated effect of gender gap is statistically significant at the: I. 5% level II. 1% level III. 0.01% level ○ A. I and II. B. I only. C. I, II, and III. D. Ill only. Construct a 95% confidence interval for the effect of gender gap. The 95% confidence interval for the effect of gender gap is ( -6.24 10.61 (Round your responses to two decimal places.)
From the sample, the average wage of women is $ per hour. (Round your response to three decimal places.) From the sample, the average wage of men is $ per hour. (Round your response to three decimal places.) 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? Wage = ^ Yo R² = = SER = Λ Yo + 1 ₁ × Female, R², SER. (Round your response to three decimal places.) (Round your response to three decimal places.) (Round your response to two decimal places.) (Round your response to one decimal place.)
Transcribed Image Text:From the sample, the average wage of women is $ per hour. (Round your response to three decimal places.) From the sample, the average wage of men is $ per hour. (Round your response to three decimal places.) 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? Wage = ^ Yo R² = = SER = Λ Yo + 1 ₁ × Female, R², SER. (Round your response to three decimal places.) (Round your response to three decimal places.) (Round your response to two decimal places.) (Round your response to one decimal place.)
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