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ECON/MGMT 201: Applied Statistics
Final Exam Practice Problems
Note that the problems only cover the material covered since the second midterm. The final will
be comprehensive, so you should review the material covered on the first two midterms.
1. You wish to test whether the reliability of your company’s product differs from the reliability
of a competitor’s product. You have collected samples and found the following:
Your Product
Competitor’s
Product
Sample Size
1200
1000
Number of Failures
83
57
Assume a 5% level of confidence. What is your conclusion? What is the 95% confidence
interval?
2. You have been asked to advise a consumer electronics company concerning its marketing
strategy. The company is considering advertisements in several different magazines. The
per-month cost of advertising is $12,000 for Time, $16,000 for Newsweek, and $20,000 for
Reader’s Digest. You have collected historical data on the response to advertisements in
those magazines and found the following:
Time
Newsweek Reader’s Digest
Month
Revenues
Revenues
Revenues
January 2000
$53,389
$102,376
$12,349
February 2000
$121,689
$124,574
$52,348
March 2000
$15,999
$112,553
$47,439
April 2000
$120,738
$59,668
$109,483
May 2000
$115,292
$45,087
$125,610
June 2000
$24,508
$101,590
$137,062
July 2000
$97,345
$69,587
$75,944
August 2000
$12,250
$28,977
$159,637
September 2000
$129,029
$26,858
$109,519
October 2000
$13,681
$39,778
$111,394
November 2000
$47,491
$28,574
$177,211
December 2000
$54,971
$101,763
$18,492
You are interested in whether advertising is more effective in one of the magazines than the
others. How might you address the problem? Which magazine (if any) is more effective
than the others? You may assume a 5% level of confidence.
3. Historically, one professor has failed 6% of the students in an introductory class while
another professor has failed 9% in the same class. 312 have taken the class from the first
professor while 220 have taken it from the second professor. Is one professor more difficult
(in terms of achieving a passing grade) than the other?
4. Suppose that new graduates from W&L earn an average of $40,000 per year with a standard
deviation of $10,000. New graduates from Stanford earn an average of $45,000 per year
with a standard deviation of $12,000. The samples include 100 people from each university.
Do Stanford graduates earn more than W&L graduates on average?
5. Suppose the average life expectancy is 74 years. A sample of 40 vegetarians found that the
average age at death was 78 with a standard deviation of 15. Do vegetarians live longer than
average? What is the 95% confidence limit? What is the 80% confidence limit? Sketch the
power curve for the test by plotting at least three points.
6. On average, a company spends $32,500 per year to maintain its buildings. This includes,
heating and electricity, so the figure can be quite volatile. The historical standard deviation
is $8,000 based on a sample size of six. A recent news article suggested that companies of
this type spend $25,000 per year on average. Should the company be alarmed?
7. A company wants to test the reliability of a new component. Assuming that the proportion of
defects is likely to be about 0.04, what sample size should be chosen so that the margin of
error (given a 95% confidence level) is 0.0005?
8. BRIEFLY discuss the similarities between hypothesis testing and detecting outliers.
9. You are interested in evaluating a product for possible sale in your store. The company has
sent 100 randomly-chosen samples for you to test. You plan to go through with the deal as
long as you believe no more than 5% of the products you subsequently purchase will be
defective. You believe a 90% confidence level is appropriate for the test. What test statistic
is appropriate? Specify the null and alternative hypotheses for the test. Sketch the power
curve for the test.
10. Two professors teach the same course. The professors give the same final exam to both
groups of students. Last term, professor A’s students averaged 75 on the final with a
standard deviation of 12. Meanwhile, professor B’s students averaged 80 on the final with a
standard deviation of 10. There were 16 students in each class. Assuming that teaching
quality can be measured by student performance, is professor B a better teacher than
professor A? Use a 10% level of significance in addressing the issue. Answer the question
by calculating the p-value. Answer the question by establishing a 90% confidence limit.
Answer the question by establishing a cutoff for the z-score or t-score (whichever is
appropriate). For each case, briefly state the logic behind the rejection decision.
11. The city council is planning a community-wide picnic. The council wants to estimate the
proportion of residents who will attend the picnic. To do so, the council will randomly select
residents and make phone calls. What is the margin of error if the council phones 30 people?
If the desired margin of error is 4% at the 95% confidence level, what sample size should the
council use?