Q1. At the end of 2008, the variance in the semiannual yields of overseas
government bond was σ2 = 0.70. A group of bond investors met at that time to
discuss future trends in overseas bond yields. Some expected the variability in
overseas bond yields to increase and others took the opposite view. The following
table shows the semiannual yields for 12 overseas countries as of March 6, 2009
(Barron’s, March 9, 2009).
Country
Australia
Belgium
Canada
Denmark
France
Germany
Italy
Japan
Netherlands
Spain
Sweden
U.K.
Yield (%)
3.98
3.78
2.95
3.55
3.44
3.08
4.51
1.32
3.53
3.9
2.48
3.76
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a. Compute the mean, variance, and standard deviation of the overseas bond yields as of March 6, 2009.
b. Develop hypotheses to test whether the sample data indicate that the variance in bond yields has changed from that at the end of 2008.
c. Use α = 0.05 to conduct the hypothesis test formulated in part (b). What is the conclusion?
d. Write a managerial statement based on the above findings.
Q2. Many smartphones, especially those of the LTE-enabled persuasion,
have been criticized for exceptionally poor battery life. Battery life
between charges for the Motorola Droid Razr Max averages 20 hours
when the primary use is talk time and 7 hours when the primary use is
Internet applications (The Wall Street Journal, March 7, 2012). Since the
mean hours for talk time usage is greater than the mean hours for Internet
usage, the question was raised as to whether the variance in hours of
usage is also greater when the primary use is talk time. Sample data
showing battery hours of use for the two applications follows.
Primary Use: Talking
35.8
22.2
8
3.8
Primary Use: Internet
14
12.5
5.4
1
4
30
32.6
12.8
8.5
10.3
16.4
15.2
1.9
4
42.5
9.9
4.7
a. Formulate hypotheses about the two population variances that can be used to determine if the population variance in battery hours of use is greater for the talk time application.
Answer:
b. What are the standard deviations of battery hours of use for the two samples?
Answer:
c. Conduct the hypothesis test. Using a 0.05 level of significance, what is your conclusion?
Answer:
d. Write a managerial statement based on the above findings.
Answer:
