Answered: A researcher wishes to study the relationship between education and income separately for individuals who have college degrees, and for those who don't. To this…

Name: A researcher wishes to study the relationship between education and in
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Description: A researcher wishes to study the relationship between education and income separately for individuals who have college degrees, and for those who don't. To this end, he interviews 100 individuals in each category. Survey results are listed in the tab

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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A researcher wishes to study the relationship between education and income separately for individuals who have college degrees, and for those who don't. To this end, he interviews 100 individuals in each category. Survey results are listed in the table below.

	non college graduates	college graduates
avg education	13 yr	18 yr
std. dev. education	2 yr	1.2 yr
S_xx	396 yr²	143 yr²
Avg. Income	$67,200	$84,950
std. dev. income	$9,400	$10,500
correlation coefficient	.25	.15

a. Use the data above to find point estimates for regression coefficients B₀^NG and B₁^NG for non-college graduates and B_o^G and B₁^G for college graduates.

b. Propose an unbiased estimator for the difference theta=B₁^G - B₁^NG in slope coefficients for the two sub-populations, and show that B(theta hat)= 0.

c. Assume that the error terms E^NG and E^G for non-graduates and graduates, respectively, are both distributed normally, with known standard deviation o_E^NG = o_E^G = $

10,000. In that case, determine the standard deviation error of theta hat, along with the shape of its distribution.

d. Using the estimator defined above, and maintaining the assumption o_E^NG = o_E^G = $10,000, test at the alpha = .05 level whether the slope coefficients, for the two sub-populations differ. State the p-value associated with this hypothesis test.

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