Economics 309             Exam Three             Fall 2003

1. (25) Write down the alternative hypothesis for each of the following null hypotheses. Indicate whether the test is a one-tailed, or two-tailed, test and suggest a test statistic for the hypothesis. How is your suggested test statistic distributed when the null hypothesis is true?
Be detailed in your answer.

(a) Ho: b 1 = 0 in the regression model Y = b(0) + b(1).X + u.
(b) Ho: b 1 ≥ 1 in the regression model Y = b(0) + b(1).X + u.
 

2. (25) Given the following information from an ordinary least squares regression, test the null hypothesis Ho: beta1 = 0.

beta1-hat = 0.37
SER* = 1.2
Σ(Xi - Xbar)^2 = 2.88
n = 10
α = Pr(type I error) = 0.05

Note: beta1 hat is the estimated coefficient, Xbar is the sample mean for X, ^2 means squared.
*Standard Error of Regression  (See text, page 240-241)

3. (50) Consider the following output from an ordinary least squares regression model.

Data: U.S. Education Department Higher Education General Information System
Dependent variable (Y): Total male and female enrolment at specific 4 year college
Independent variables (the Xs):

PUBLIC    (0,1) indicator. =1 if public, =0 if private
PADM       probability of admission, ranges from 0-100.
TUITN       posted tuition for specific college
AVFAID   average value of financial aid given to students
SFRAT     faculty/student ratio for teaching
QUAL       measure of college quality, average SAT score of incoming freshmen
RTEACH  ratio of total tuition to total teaching expenditures at college.

Model: regresses enrolment (variable name = TENROL) on factors that may effect enrolment (mainly demand factors)
The estimates of the model are provided in the computer program output table.

(a) Which of the coefficients are significantly different from zero at the 5% level? Make a list and explain how you came to your conclusion, but don’t perform a formal test for each coefficient.
(b) What is the effect of tuition on enrolment? Perform a statistical test of the appropriate hypothesis.
(c) What is the effect of quality on enrolment? Set up and test the appropriate hypothesis.
(d) What does this regression model tell you? Write a few paragraphs discussing the results in light of the model presented here.

SAS econometric software output table for question 3.

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