Question

In February, the Pew Internet & American life project conducted a survey that included several questions about how Internet users feel about search engines and other websites collecting information about them and using this information either to shape search results or target advertising to them. In one question, participants were asked, "If a search engine kept track of what you search for, and then used that information to personalize your future search results, how would you feel about that?" Respondents could indicate either "Would not be okay with it because you feel it is an invasion of your privacy" or "Would be okay with it, even if it means they are gathering information about you." Probabilities of responses by age group are summarized in the following table.

Age Not Okay Okay

18-29 0.1475 0.0605

30-49 0.2283 0.0906

50+ 0.4005 0.0726

Round your answers to four decimal places.

a. What is the probability a survey respondent will say she or he is not okay with this practice?

b.  Given a respondent is 30-49 years old, what is the probability the respondent will say she or he is okay with this practice?

c. Given a respondent says she or he is not okay with the practice, what is the probability the respondent is 50+ years old?

d.  Is the attitude about this practice independent of the age of the respondent? Why or why not?

The probability that a respondent is 30-49 , given that she or he is okay with the practice is _______

The probability that a respondent is okay is ___________

Since the numbers (do/do not) equal the events are said to be (dependent/independent)

e. Do attitudes toward this practice for respondents who are 18-29 years old and respondents who are 50+ years old differ?

(Yes, No)  because the probability that a respondent is not okay with the practice given that he or she is 18-29 is _____ and the probability that a respondent is okay with the practice given that he or she is not 50+ is _________.

Answer 1

age	not ok	ok	total
18-29	0.1475	0.0605	0.208
30-49	0.2283	0.0906	0.3189
50+	0.4005	0.0726	0.4731
total	0.7763	0.2237	1

a)

  probability a survey respondent will say she or he is not okay with this practice =0.7763

b)

probability the respondent will say she or he is okay with this practice given 30-49 yrs old

=0.0906/0.3189=0.2841

c)

probability the respondent is 50+ years old given not ok=0.4005/0.7763=0.5159

d)

The probability that a respondent is 30-49 , given that she or he is okay with the practice is

=0.0906/0.2237=0.4050

The probability that a respondent is okay is =0.2237

Since the numbers do not equal the events are said to be dependent

e)Yes because the probability that a respondent is not okay with the practice given that he or she is 18-29 is 0.1475/0.2080=0.7091

and the probability that a respondent is okay with the practice given that he or she is not 50+ is 0.2868