4.2.22 Question Help Answers Quickly Do people of different age groups differ in

Question

4.2.22 Question Help Answers Quickly Do people of different age groups differ in their response to email messages? A survey reported that 72.9% of users over 70 years of age believe that email messages should be answered quickly, as compared to 50.6% of users 13 to 50 years old. Suppose that the survey was based on 1,000 users over 70 years of age and 1,000 users 13 to 50 years old. The table to the right summarizes the results. Complete parts (a) through (c) Total Age Yes No Total 13-50 506 494 1000 Over 70 729 271 1000 1235 765 2000 a. Suppose you know that the respondent is between 13 and 50 years old. What is the probability that he or she answers quickly? The probability that he or she answers quickly is .506 (Simplify your answer.) b. Suppose you know that the respondent is over 70 years old. What is the probability that he or she answers quickly? The probability that he or she answers quickly is (Simplify your answer.)

Explanation / Answer

a)

p( Answer quickly | respondents is between 10 and 50 years)

= p( Answer quickly AND respondents is between 10 and 50 years)/ p(respondents is between 10 and 50 years)

= 506 / 1000

= 0.506

b)

p( Answer quickly | respondents is over 70 years )

= p( Answer quickly AND respondents is over 70 years)/ p(respondents is over 70 years)

= 729 / 1000

= 0.729

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