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Expected Frequency/independence of attributes

Problem 12.1 For this problem use the following contingency table:

A B Total
1 20 30 50
2 30 45 75
Total 50 75 125

a. Find the expected frequency for each cell.

b. Compare the observed and expected frequencies in each cell.

c. Compare the X2 statistic. Is it significant at alpha () = .05.

Problem 11.13 A survey for Internet users in the United States, Australia, and Europe studied whether those who downloaded music subsequently purchased a CD or tape of the music ("net Music Inspires Buying." USA Today, January 23, 2001, 1A). The survey reported that 77% of Americans, 78% of Australians, and 54% of Europeans who downloaded music get inspired to purchase the CD or tape of music. Suppose the survey was based on a sample of 500 Americans, 250 Australians, and 500 Europeans.

a. At the .05 significance level, determine whether there is a significant difference in the proportion of Americans, Australians & Europeans who get inspired to purchase a CD or tape of the music?

b. Find the p-value and interpret its meaning.


Problem 11.23 An article in USA Today reported on what most want in a car to make driving time as enjoyable as possible ("Drivers Just Want to Have Fun," USA Today, May 25, 2000). Suppose the results were based on a survey of 1000 respondents and also considered whether they primarily drove a sedan, sporty car, or sport utility vehicle. The results are cross-classified into the following table:
Type of Car Driven
TECHNOLOGY DESIRED Sedan Sporty Car Sports Utility Vehicle
CD Player/Changer 178 58 54
Quality Stereo System 80 54 46
Cell Phone 100 8 22
Global Positioning System 70 4 16
Movie/Game Player 68 6 6
Internet Access 24 6 10
Radar Detector 16 34 20
Don't Know 80 26 14

a. At the .05 significance level is there evidence of a significant relationship between the type of technology desired and the type of car driven?

Problem 10.33 A vice president for marketing recently recruited 20 outstanding college graduates to be trained in sales and management. The 20 individuals are randomly assigned, 10 each to one of two groups. A "traditional" method of training (T) is used in one group and an "Experimental" training method is used in the other. After six months on the job, the vice president ranks the individuals on the basis of their performance from 1 (worst) to 20 (best) with eth following results:

T 1 2 3 5 9 10 12 13 14 15
E 4 6 7 8 11 16 17 18 19 20

The survey also evaluated purchase decisions at other prices. These results are summarized in the following contingency table:

Is there a difference in performance based on the two methods? (Use  = .05)

Problem 11.41 An industrial psychologist wants to test whether the reaction times of assembly line workers are equivalent under three different learning methods. From a group of 25 new employees, 9 are randomly assigned to method "A," 8 to method "B," and 8 to method "C." After the learning period, the workers are given a task to complete, and their reaction times are measured. The rankings of reaction times from 1 (fastest) to 25 (slowest are in the table below:

Reaction Time by Group
2 1 5
3 6 7
4 8 11
9 15 12
10 16 13
14 17 18
19 21 24
20 22 25

Is there evidence of a significant difference in median reaction times for these learning methods" (use  = .01)?

Problem 11.53 An increasing number of employees are exploring the Internet for savings in business travel. An article (D. Rosato and S. Khan, "Net Surfing Nets Savings for Business Travelers," USA Today, March 7, 20000, 1B-2B) reported on the results of 400 corporate travel managers. Suppose that a contingency table of whether employees researched airline ticket prices and booked airline tickets on the Internet revealed the following results.

Booked Airline Tickets on the Internet
Researched Airline Ticket Prices on the Internet Yes No Total
Yes 88 124 212
No 20 168 188
Total 108 292 400

a. At the .05 significance level is there a significant relationship between researching airline prices on the Internet and booking airline prices on the Internet and booking airline tickets on the Internet?

b. Determine the p-value and inter[prêt its meaning.

See attached file for full problem description.

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Solution Summary

Expected Frequency/independence of attributes, t-test, chi-square are evaluated in the following problems.