econ stats

ECON/MGMT 201: Applied Statistics

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:

Month	Time Revenues	Newsweek Revenues	Reader’s Digest 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. 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. 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.

74

1

80

population mean

power