1. Using data from 2013 on 64 black females, the estimated log-linear regression between WAGE (earn- ings per hour, in $) and years of education, EDUC is ln(WAGE) = 1.58+0.09EDUC. The reported t-statistic for the slope coefficient is 3.95. (a) Test at the 5% level of significance, the null hypothesis that the return to an additional year of education is equal to 8% against the alternative that the rate of return to education is more than 8%. In your answer, show (i) the formal null and alternative hypotheses, (ii) the test statistic and its distribution under the null hypothesis, (iii) the critical value from the t table and the rejection region (in a figure), (iv) the calculated value of the test statistic, and (v) state your conclusion, with its economic interpretation. [Hint: From the information you should be able to figure out the standard error of the slope coefficient (se(b₂)). Then, with the calculated standard error, you should be able to find the t statistic.] (b) Construct a 95% interval estimate for the return to an additional year of education and state its interpretation.
1. Using data from 2013 on 64 black females, the estimated log-linear regression between WAGE (earn- ings per hour, in $) and years of education, EDUC is ln(WAGE) = 1.58+0.09EDUC. The reported t-statistic for the slope coefficient is 3.95. (a) Test at the 5% level of significance, the null hypothesis that the return to an additional year of education is equal to 8% against the alternative that the rate of return to education is more than 8%. In your answer, show (i) the formal null and alternative hypotheses, (ii) the test statistic and its distribution under the null hypothesis, (iii) the critical value from the t table and the rejection region (in a figure), (iv) the calculated value of the test statistic, and (v) state your conclusion, with its economic interpretation. [Hint: From the information you should be able to figure out the standard error of the slope coefficient (se(b₂)). Then, with the calculated standard error, you should be able to find the t statistic.] (b) Construct a 95% interval estimate for the return to an additional year of education and state its interpretation.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![1. Using data from 2013 on 64 black females, the estimated log-linear regression between WAGE (earn-
ings per hour, in $) and years of education, EDUC is ln(WAGE) = 1.58+0.09EDUC. The reported
t-statistic for the slope coefficient is 3.95.
(a) Test at the 5% level of significance, the null hypothesis that the return to an additional year of
education is equal to 8% against the alternative that the rate of return to education is more than
8%. In your answer, show (i) the formal null and alternative hypotheses, (ii) the test statistic and
its distribution under the null hypothesis, (iii) the critical value from the t table and the rejection
region (in a figure), (iv) the calculated value of the test statistic, and (v) state your conclusion,
with its economic interpretation. [Hint: From the information you should be able to figure out
the standard error of the slope coefficient (se(b₂)). Then, with the calculated standard error, you
should be able to find the t statistic.]
(b) Construct a 95% interval estimate for the return to an additional year of education and state its
interpretation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ec7f5aa-860a-4129-9ae6-a6b79946e954%2F1e50fdf0-8c74-4daa-8e0f-02783d947f3b%2F4l0ml7k_processed.png&w=3840&q=75)
Transcribed Image Text:1. Using data from 2013 on 64 black females, the estimated log-linear regression between WAGE (earn-
ings per hour, in $) and years of education, EDUC is ln(WAGE) = 1.58+0.09EDUC. The reported
t-statistic for the slope coefficient is 3.95.
(a) Test at the 5% level of significance, the null hypothesis that the return to an additional year of
education is equal to 8% against the alternative that the rate of return to education is more than
8%. In your answer, show (i) the formal null and alternative hypotheses, (ii) the test statistic and
its distribution under the null hypothesis, (iii) the critical value from the t table and the rejection
region (in a figure), (iv) the calculated value of the test statistic, and (v) state your conclusion,
with its economic interpretation. [Hint: From the information you should be able to figure out
the standard error of the slope coefficient (se(b₂)). Then, with the calculated standard error, you
should be able to find the t statistic.]
(b) Construct a 95% interval estimate for the return to an additional year of education and state its
interpretation.
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