Question

Where wage is in 1000's of dollars. Now suppose that your econometrics give you the to Wage = Bo + Bi Education + e that your econometrics give you the following results: Constant Education Coefficient 45.32 10.32 5 Standard Error 30.65 2.35 N=42 a. Estimate a 95% confidence interval for a 95% confidence interval for B.. Show your work carefully. What does this ence interval tell us about the relationship between education and wages? (2 marks) b. Test at the 99% level the at the 99% level the null hypothesis that B, is zero, versus the alternative hypothesis Its not. Show your work and write the result clearly. Also write your conclusion. Interpret your result in words using economic theory. (3 marks) C. Test at the 95% level the null hypothesis that Bo is zero, versus the alternative that it's positive. Show your work, the result and write your conclusion. Explain in words what does the conclusion mean. (2 marks) d. Your manager thinks that 1 additional year of education will lead to an increase in wages by 1500 dollars. Choose an alternative hypothesis and explain your choice. Does your estimated relationship support this claim? Use a 5% significance level. (3 marks)

Answer 1

Ansuler nean- sample size is more than 30 therefore we will use z test. Critical z value for 95% CI is 1.96 CI is given as below = (sample mean - critical z x standard erar, Sample mean + critical 2 x standard sort) = (10.32 -1.96*2.35, 10.32+1.96X2,35) - (5.71,14.93) Therefore, we can clearly say that coefficient of Education is statistically different than o. It is positive relationship between mages and Education as all possible values taken by Gefficient of education is positive CS Scanned with CamScanner

Critical z value for 99%. CI is 2.58 calculated a value for 99% CI is 10.32 (2.35 - 4.39 Hence when calculated z value > critical z Value we can reject null hypothesis and Can Say as per guen sample we are good to say that coefficient of B1 is statistically different than o. It means education is deciding and very important variable to decide wages of an individual. Critical z value for 95% CI is 1.96 calculated a value for 95% CI is 45.32/30.65 = 1.48 Scanned with CamScanner

Hence, when calculated a value a critical z lature we can reject null hypothesis and can say os per given sample we are good to say that Coefficient of B1 is not statistically different than o. It means we can remove drift term from regression of wages as it has no statistical importance in an equation. calculated z = 10.32-1.5/2.35 -8.82(2.35 = 3.753 critical z for 5% significance level = 1.96 Hence, we can reject that null that 1 additional year increase in education could lead to $1500 increase in wages it would be surely more than that. CS Scanned with CamScanner