Economics 391 (Spring 2013) Professor Lamarche, University of Kentucky Sample Final Exam Questions 1. Suppose you estimate a model obtaining, wage = XXXXXXXXXX × educ + 2.27 × female were wage is...

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Economics 391 (Spring 2013) Professor Lamarche, University of Kentucky
Sample Final Exam Questions
1. Suppose you estimate a model obtaining,
wage = 0.620 + 0.506 × educ + 2.27 × female
were wage is measured in dollars/hour and female is a binary variable that is equal to one if the person is a female and zero if the person is a male. The standard errors are 0.67, 0.050 and 0.279, respectively.
(a) Is the ‘gender gap’ significantly different from zero? (b) What is the predicted wage for a female worker with 10 years of education with 16 years? (c) How many years of education a male needs to obtain the hourly wage that a female with 16 years earns?
2. Consider you estimate the following regression model,
y = a + ßx + u
where y is the dependent variable, x is the independent variable and u is the error term.
(a) Explain the difference between correlation and regression and explain the assumptions of the regression model. (b) What are the interpretation of a and ß? (c) How would you estimate the unknown population parameters? (d) What are the statistical properties of the method you proposed?
3. Suppose that the null hypothesis is H0 : = 1000 and the alternative hypothesis H1 : =? 1000. Assuming s = 200, n = 100, X¯ = 980, and a = 0.01, calculate



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Economics 391 (Spring 2013) Professor Lamarche, University of Kentucky Sample Final Exam Questions 1. Suppose you estimate a model obtaining, wage= 0.620+0.506×educ+2.27×female were wage is measured in dollars/hour and female is a binary variable that is equal to one if the person is a female and zero if the person is a male. The standard errors are 0.67, 0.050 and 0.279, respectively. (a) Is the ‘gender gap’ signi?cantly di?erent from zero? (b) What is the predicted wage for a female worker with 10 years of education with 16 years? (c) How many years of education a male needs to obtain the hourly wage that a female with 16 years earns? 2. Consider you estimate the following regression model, y = a+ßx+u where y is the dependent variable, x is the independent variable and u is the error term. (a) Explain the di?erence between correlation and regression and explain the assumptions of the regression model. (b) What are the interpretation of a and ß? (c) How would you estimate the unknown population parameters? (d) What are the statistical properties of the method you proposed? 3. SupposethatthenullhypothesisisH : µ = 1000andthealternativehypothesis 0 ¯ H : µ = 6 1000. Assuming s = 200, n = 100, X = 980, and a = 0.01, calculate 1Economics 391 (Spring 2013) Professor Lamarche, University of Kentucky the value of the test statistic, set up the rejection region, and determine the p-value. Would you reject the null hypothesis? 4. Consider the return to education model, lnw =ß +ß educ+u it 0 1 where the dependent variable is the logarithm of wages and the independent variables are years of education (x ) and years of experience (x ). 1 2 (a) Suggest a method to estimate the equation of interest. (b) Using the method you proposed before, you obtain the regression results called “SUMMARY OUTPUT # 1” (please see the last pages). What is ˆ ˆ the interpretation of the coe?cients ß and ß ? 0 1 (c) Test if education has a signi?cant e?ect on log of wages. (State clearly the null...



Answered Same DayDec 22, 2021

Answer To: Economics 391 (Spring 2013) Professor Lamarche, University of Kentucky Sample Final Exam Questions...

David answered on Dec 22 2021
122 Votes
Solution 1:
a) Null Hypothesis (Ho): Gender gap is not significantly different from zero.
Alternative Hypothesis (Ha): Gender gap is significantly different from zero.
T-st
atistics = Coefficient/standard error
=2.27/0.279
= 8.14
P-value = 0.000
Since p-value is approximately zero, we reject the null hypothesis.
There is sufficient evidence to conclude that Gender gap is significantly different from zero.
b) When educ =10 and female = 1
Wage = 0.620 + 0.506 x 10 + 2.27 x 1
= 7.95
When educ =16 and female = 1
Wage = 0.620 + 0.506 x 16 + 2.27 x 1
= 10.986
c) When wage = 10.986, male = 0
10.986 = 0.620 + 0.506 x educ + 2.27 x 0
Educ = 20.49 ~ 20.5 years
Solution 2:
a) Correlation measures the strength of linear association between the variables whereas regression measures the form of linear association which predicts Y from the value of X. The assumptions are:- i) Linearity, ii) Independence, iii) Homoscedasticity and iv) Normality.
b) α and β are the coefficients of X and indicates the effect of change in dependent variable caused by the change in independent variable.
c) The unknown population parameters are estimated using interval estimation or point estimation.
d) The statistical properties are:- i) Consistency, ii) Unbiasedness and iii) Efficiency.
Solution 3:
Value of test statistic
Z = (X-bar - µ)/ (σ/√n)
= (980 – 1000)/ (200/√100)
= -1
Using Z-tables, the critical value is
Z (0.01/2) = Z (0.005) = ± 2.576
Rejection region: If Z < -2.576 or Z > 2.576, null hypothesis is rejected or accepted otherwise.
P [Z ≠ -1] = 2*0.1587 = 0.3173
Since test statistics lie within the critical values, we fail to reject the null hypothesis....
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