05 Jun Question Economics 102 Problem Set #3
Question
Economics 102
Problem Set #3
Due Saturday, July 11 before 10 p.m. 20 points possible
Department of Economics
Professor Siegler
UC Davis
Summer 2015
Be sure to submit a self-contained Word file with all of the calculations, explanations, etc. Also, attach any Excel and GRETL files.
1.Testing Proportions (3 points)
Suppose someone claims that at least 90 percent of U.S. households have internet access. To test this claim, you randomly sample 100 U.S. households and find that 81 percent of your sample has internet access. What are the null and alternative hypotheses? What is the value of your test statistic? Can you reject the null hypothesis at the five-percent level of significance? Can you reject the null hypothesis at the one-percent level of significance? Show your work and explain.
2.Correlation and Simple Regression the Old-Fashioned Way (12 points)
The problem asks you to compute the sample correlation coefficient (___) and estimate
the regression coefficients with ordinary least squares (OLS) for the model
(__= _ + ____+_) using the data below, but without using Excel or GRETL (except to get critical values or p-values, and to check your work). That is, use the Equation Editor in Word to show all of your calculations, similar to the example done in lecture.
Y X
4 1
8 3
5 2
7 2
A. (1 point) Compute and report the sample correlation coefficient (___).
B. (2 points) Can you reject the null hypothesis that the true population correlation coefficient is zero at the ten-percent level of significance? Can you reject the null at the five-percent level of significance? Show your work and explain.
C. (2 points) Show all of your work in computing the OLS estimates_ and___.
D. (2 points) Show all of your work in computing the coefficient of determination (R2) and interpret its meaning.
E. (2 points) At the ten-percent level of significance, can you reject the null hypothesis that__= 0? Can you reject the null hypothesis at the five-percent level of significance? Show your work and explain.
1
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