Reference no: EM132839996
Do people of different age groups differ in their response to messages? A survey by the Center for the Digital Future of the University of Southern California (data extracted from A. Mindlin, "Older E-mail 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 messages should be answered quickly, as compared to 53.6% of 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
12-50 over 70 total
Answers quickly
yes 536 707 1243
no 464 293 757
total 1000 1000 2000
(a) Define two variables used in the survey data. Define the sample space of each variable.
(b) Suppose a respondent is randomly selected, what is the probability that he or she is from age 12~50?
(c) Given that a respondent from age 12~50 is selected, what is the probability that the respondent believe messages should be answered quickly?
(d) Are the two variables in (a) are independent? Explain based on probability values.
(e) If 15 respondents out of 2,000 survey respondents were randomly selected as a sample, what is the probability that 8 respondents from age 12~50 are included in the sample? (use the binomial distribution with the parameter ? from the survey data