Question

1. Suppose that you ran the following regression:

Wage = Bo + B1Education +e

Where wage is in 1000's of dollars. Now Suppose that your econometrics give you the following results

	Coefficient	Standard Error
Constant	45.32	30.65
Education	10.32	2.35

N= 42

1. Estimate a 95% confidence interval for B1 Show your work carefully. What does this Confidence interval tell us about the relationship between education and wages?

2. Test at the 99% level the null hypothesis that B1 is zero, versus the alternative hypothesis that it's not Show your work and write the result clearly. Also write your conclusion. Interpret your result in words using economic theory.

3. 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.

4. 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.

Answer 1

Answer A)

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 * Standard error,Sample mean + Critical z * Standard error)

=(10.32-1.96*2.35,10.32+1.96*2.35)=(5.71,14.93)

Therefore we can clearly say that Coefficient of Education is statistically different than zero

It is positive relationship between Wages & Education as all possible values taken by coefficient of education is positive

Answer B)

Critical z value for 99% CI is 2.58

Calculated z valuw 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 givne sample we are good to say that coefficient of B1 is staistically different than 0

It means education is deciding and very important variable to decide wages of an individual

Answer C)

Critical z value for 95% CI is 1.96

Calculated z valuw for 95% CI is 45.32/30.65 =1.48

Hence when Calculated Z value < Critical Z value we can not reject null hypothesis and can say as per givne sample we are good to say that coefficient of B1 is not staistically different than 0

It means we can remove drift term from regression of wages as it has no statistical importance in an equation

Answer D)

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 the null that 1 additional year increase in education could lead to $1.5k increase in wages It would be surely more than that.