UNC-Wilmington
Department of Economics and Finance
Homework 8
ECN 377
Dr. Chris Dumas
(Due Thurs, Sept. 24)
Multiple Choice
1) Your junior research associate comes into your office and tells you that he thinks stock prices are becoming more volatile
(i.e., more variable). He says that the variance of stock prices last year was 645.3. In addition to the given number from your
associate, you have a random sample of stock price data for this year from which you can calculate this year's sample
variance. Which type of hypothesis test should he conduct to determine whether stock prices are becoming more volatile?
a) independent samples t-test
b) Chi-square test
c) hypothesis test of proportions
d) F-test
2) You think that perhaps housing prices are becoming more volatile (i.e., more variable). Last year the variance of housing
prices was 645.3. In addition to this given number from last year, you have a random sample of housing price data for this
year from which you can calculate this year's sample variance. Which type of hypothesis test should you conduct to
determine whether housing prices are becoming more volatile?
a) independent samples t-test
b) Chi-square test
c) hypothesis test of proportions
d) F-test
3) You think that perhaps housing prices are more volatile (i.e., more variable) in the USA compared to Japan. You take a
random sample of house prices from each country and calculate a sample variance for each sample. Which type of
hypothesis test should you conduct to determine whether housing prices are more volatile in the USA compared to Japan?
a) independent samples t-test
b) Chi-square test
c) hypothesis test of proportions
d) F-test
Problem Section
4) In investment analysis, the variance in the return on an investment is a critical piece of information. Suppose that the
variance in the return on investment A has been 2.34 in the past, but suppose a recent event in the market may have affected
the return on investment A. Based on a sample size of 41 randomly sampled observations on this investment, the sample
variance in its return now appears to be 2.39. Use the appropriate hypothesis test to determine whether there has been a
significant increase in the variance of the return for investment A. Assume a Confidence Level of 95%. SHOW YOUR
WORK, including the null hypothesis and the alternative hypothesis that you are testing!
5) Suppose you also have a sample of 21 randomly sampled observations on investment B, and the sample variance in its
return is currently 3.78 . Based on your results from the problem above, conduct the appropriate hypothesis test to determine
whether the variance in investment B is currently significantly larger than the variance in investment A. Assume a
Confidence Level of 95%. SHOW YOUR WORK, including the null hypothesis and the alternative hypothesis that you are
testing!
6) Suppose your consulting firm is hired to determine whether there is more income inequality in the southern United States
relative to the northern United States. To assess this, you collect data on mean household income for a random sample of 260
counties in the northern United States and a random sample of 140 counties in the southern U.S. The sample variance in
mean household income for the northern counties is 1520, and the sample variance for the southern states is 2467. Use the
appropriate hypothesis test to determine whether there is a statistically significant difference in the variance of household
income between northern and southern states. Assume a Confidence Level of 95%. SHOW YOUR WORK, including the
null hypothesis and the alternative hypothesis that you are testing!
7) You work for a large auto company that sells autos in Europe and China. Your boss wants to know whether auto prices
are more variable in Chinese cities relative to European cities. You have good data on your auto sales in European cities, and
you know that the variance in auto prices in those cities is 4500. Your data from China is not as good. You have data on
auto prices in a sample of 13 Chinese cities. In these cities, the sample variance of auto prices is 6300. Use the appropriate
hypothesis test to determine whether the variance in auto prices in Chinese cities is significantly larger than the variance in
European cities. Assume a Confidence Level of 95%. SHOW YOUR WORK, including the null hypothesis and the
alternative hypothesis that you are testing!