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In this exercise we examine which factors might influence the wages of employees. To do so, the variable wage is regressed on the variables educ, tenure, tensq, female, married, and m_female.Table 1: Descriptive StatisticsVariable Explanationwage Average hourly wage (in €)educ Years of educationtenure Employment duration (current employer)tensq = tenure × tenurefemale dummy (= 1 if female)married dummy (= 1 if married)m_female      Interaction term (= married × female)The corresponding Stata output is:Source | SS df MS N. of obs. = 526 + F(6, 519) = 57.23 Model | 2851.181 6 475.197 Prob > F = 0.000 Residual | 4309.233 519 8.303 R-squared = 0.398 + Adj. R-sq. = 0.391 Total | 7160.414 525 13.639 Root MSE = 2.882 wage | Coef. S. Err. t-stat. P > |t| [95% Conf. Int.] + educ |0.522 0.046 ? ? ? ? tenure | 0.263 0.046 5.69 0.000 0.172 0.354 tensq | -0.005 0.002 -2.77 0.006 -0.008 -0.001 female | -0.321 0.408 -0.79 0.431 -1.123 0.480 married | 1.807 0.389 4.65 0.000 1.043 2.571 m_female | -2.326 0.526 ? ? ? ? _cons | -2.012 0.662 -3.04 0.002 -3.313 -0.711 Reference: Wooldridge, J. (2013). Introductory Econometrics, 5E. © 2013 South-Western, a part of Cengage, Inc. Reproduced by permission. www.cengage.com/permissions.Does educ have a significant relationship with the outcome wage? State the associated null hypothesis and alternative hypothesis for the coefficient βeduc. Also, determine its statistical significance at the 5 percent significance level in a two-sided test. Which one is the correct answer?Answer 1H0:   vs.   H1: c(0.05, 526-6-1) = 1.645⇒ t > c⇒ H0 can be rejected at the 5 percent significance level.Answer 2H0:   vs.   H1: c(0.05, 526-6-1) = 1.645⇒ t > c⇒ H0 can be rejected at the 5 percent significance level.Answer 3H0:   vs.   H1: c(0.05, 526-6-1) = 1.960⇒ t > c⇒ H0 can be rejected at the 5 percent significance level.Answer 4H0:   vs.   H1: c(0.05, 526-6-1) = 1.960⇒ t > c⇒ H0 can be rejected at the 5 percent significance level.

Question

In this exercise we examine which factors might influence the wages of employees. To do so, the variable wage is regressed on the variables educ, tenure, tensq, female, married, and m_female.Table 1: Descriptive StatisticsVariable Explanationwage Average hourly wage (in €)educ Years of educationtenure Employment duration (current employer)tensq = tenure × tenurefemale dummy (= 1 if female)married dummy (= 1 if married)m_female      Interaction term (= married × female)The corresponding Stata output is:Source | SS df MS N. of obs. = 526 + F(6, 519) = 57.23 Model | 2851.181 6 475.197 Prob > F = 0.000 Residual | 4309.233 519 8.303 R-squared = 0.398 + Adj. R-sq. = 0.391 Total | 7160.414 525 13.639 Root MSE = 2.882 wage | Coef. S. Err. t-stat. P > |t| [95% Conf. Int.] + educ |0.522 0.046 ? ? ? ? tenure | 0.263 0.046 5.69 0.000 0.172 0.354 tensq | -0.005 0.002 -2.77 0.006 -0.008 -0.001 female | -0.321 0.408 -0.79 0.431 -1.123 0.480 married | 1.807 0.389 4.65 0.000 1.043 2.571 m_female | -2.326 0.526 ? ? ? ? _cons | -2.012 0.662 -3.04 0.002 -3.313 -0.711 Reference: Wooldridge, J. (2013). Introductory Econometrics, 5E. © 2013 South-Western, a part of Cengage, Inc. Reproduced by permission. www.cengage.com/permissions.Does educ have a significant relationship with the outcome wage? State the associated null hypothesis and alternative hypothesis for the coefficient βeduc. Also, determine its statistical significance at the 5 percent significance level in a two-sided test. Which one is the correct answer?Answer 1H0:   vs.   H1: c(0.05, 526-6-1) = 1.645⇒ t > c⇒ H0 can be rejected at the 5 percent significance level.Answer 2H0:   vs.   H1: c(0.05, 526-6-1) = 1.645⇒ t > c⇒ H0 can be rejected at the 5 percent significance level.Answer 3H0:   vs.   H1: c(0.05, 526-6-1) = 1.960⇒ t > c⇒ H0 can be rejected at the 5 percent significance level.Answer 4H0:   vs.   H1: c(0.05, 526-6-1) = 1.960⇒ t > c⇒ H0 can be rejected at the 5 percent significance level.

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Solution

The question is asking for the null hypothesis and alternative hypothesis for the coefficient βeduc, and whether it has a significant relationship with the outcome wage at the 5 percent significance level in a two-sided test.

The null hypothesis (H0) is that the coefficient βeduc is equal to zero, meaning that there is no relationship between the variable educ and the outcome wage. The alternative hypothesis (H1) is that the coefficient βeduc is not equal to zero, meaning that there is a relationship between the variable educ and the outcome wage.

The t-statistic for the variable educ is not given in the question, but we can use the critical value for a two-sided test at the 5 percent significance level, which is 1.96 (or -1.96 for the lower tail). If the absolute value of the t-statistic is greater than 1.96, we can reject the null hypothesis and conclude that educ has a significant relationship with wage.

Therefore, the correct answer would be:

Answer 3 H0: βeduc = 0 vs. H1: βeduc ≠ 0 c(0.05, 526-6-1) = 1.960 ⇒ t > c ⇒ H0 can be rejected at the 5 percent significance level.

or

Answer 4 H0: βeduc = 0 vs. H1: βeduc ≠ 0 c(0.05, 526-6-1) = 1.960 ⇒ t > c ⇒ H0 can be rejected at the 5 percent significance level.

However, without the t-statistic for the variable educ, we cannot definitively determine whether the null hypothesis can be rejected.

This problem has been solved

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