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# Events Relations in Statistics

1. According to an Ipsos poll, the perception of unfairness in the U.S. tax code is spread fairly evenly across income groups, age groups, and education levels. In an April 2006 survey of 1,005 adults, Ipsos reported that almost 60% of all people said the code is unfair, whereas slightly more than 60% of those making more than \$50,000 viewed the code as unfair("People Cry Unfairness, " The Cincinnati Enquirer, April 16, 2006, p.A8). Suppose that the following contingency table represents the specific breakdown of responses:
Income Level
U.S. Tax Code Less Than \$50,000 More than \$50,000 Total
Fair 225 180 405 225 180 405
Unfair 280 320 600 280 320 600
Total 505 500 1,005
a. Give an example of a simple event
b. Give an example of a joint event
c. What is the complement of "tax code is fair"?
d. Why is "tax code is fair and makes less than \$50,000" a joint event?

2. Do people of different age group differ in their response to e-mail message? A survey by the Center for the Digital Future of the University of Southern California (data extracted from A. Mindlin, "Older Email Users Favor Fast Replies, " The New York Times, July 14, 2008, p.B3) reported that 70.7% of users over 70 years of age believe that e-mail messages should be answered quickly, as compared to 53.6% old users 12 to 50 years old. Suppose that the survey was based on 1,000 users over 70 years of age and 1,000 users 12 to 50 years old. The following table summarizes the results:

Age of Respondents
Answers Quickly 12-50 Over 70 Total
Yes 536 707 1, 243
No 464 293 757
Total 1,000 1,000 2,000

a. Suppose you know the respondent is between 12 and 50 years old. What is the probability that he or she answers quickly?
b. Suppose you know that the respondent is over 70 years old. What is the probability that he or she answers quickly?
c. Are the two events, answers quickly and age, independent? Explain
For each part (a) through c) show all of your steps and define your terms. Don't simply give the answers. I want explanations.

#### Solution Preview

Hi, below is my answer. I will appreciate if you can award me bonus credits.

1. a. Give an example of a simple event
A simple event is the one of a single outcome. Example: People who made more than \$50,000

b. Give an example of a joint event
A joint event is the one of at least two outcomes. Example: The US code is unfair along with people making more than \$50,000.

c. What is the complement of "tax code ...

#### Solution Summary

The solution gives detailed steps on answering questions about relations between two events. All formula, concepts, and calculations are shown and explained.

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