Economics 102
Practice Problem Set 3
Due in Canvas on Monday, July 16 before 10 p.m.
Department of Economics Professor Siegler
UC Davis Summer 2018
1. Two-Sample Univariate Hypothesis Testing for Means by Hand
Consider a random sample of 10 people, 5 of whom graduated from UC Davis
with a degree in Managerial Economics and 5 of whom graduated from UC
Davis with a degree in Economics (all graduated at the same time). Several years
later, their hourly earnings are reported below:
Economics
Managerial
Economics
$45 $20
$65 $55
$35 $40
$45 $40
$85 $20
At the 10-percent level of significance, can you conclude that there is a difference
in hourly earnings between economics majors and managerial economics majors?
What are the null and alternative hypotheses? What test statistic should you use
for this test and why? Be sure to show all of your calculations and to interpret
your findings. That is, while you can use R to check your work, you must show
all of the calculations below “by hand.”
2. Two-Sample Hypothesis Testing with Proportions
A. Suppose that researchers want to test the effectiveness of a new anti-
anxiety medication. In clinical testing, 140 out of 200 people taking the
medication do not report symptoms of anxiety. Of the people receiving a
placebo, 60 out of 100 individuals do not report symptoms of anxiety. Is
the medication effective at reducing anxiety? Test this claim using the 5-
percent level of significance. Show your work and explain. Do this part
of the question “by hand.”
2
B. Use the prop.test() command in R to check your work. Note that R
reports the chi-squared version of the test, so square your Z-statistic from
Part A above and it should equal the value of the chi-squared statistic
which R reports. Use help(prop.test) to learn about how to use the
command. The p-values from Part A and Part B should be identical.
3. Body Temperatures by Gender
Consider the file temperaturesbygender.csv, which contains body
temperatures in degrees Fahrenheit for 65 males and 65 females. Note that you
should reorganize the data in Excel before you try to import it into R.
A. Is there a difference in the variances of male and female body
temperatures? Test using the 5-percent level of significance.
B. Is there a difference in mean body temperatures between men and women
at the 5-percent level of significance?
4. Bivariate Hypothesis Testing with Correlation by Hand
Final Exam Grade (GPA 4-point scale) Hours of Study
3 4
4 6
2 3
2 2
3 2
4 7
A. Compute the sample correlation coefficient between final exam grades
and hours of study on the day prior to the final exam for a random sample
of 6 students in a class.
B. Test the null hypothesis g1834g2868:uni0009g2025 = 0 versus the alternative hypothesis
g1834g2869:uni0009g2025 ≠ 0. Can you reject the null hypothesis at the 5-percent level of
significance? Can you reject the null at the 1-percent level of significance?
Show your work and explain.
C. Use cor.test() in R to check your work in Parts A and B above.