Common Sense Media surveyed 1000 teens and 1000 parents of teens to learn about how teens are using social networking sites such as Facebook and MySpace (“Teens Show, Tell Too Much Online,” San Francisco Chronicle, August 10, 2009). The two samples were independently selected and were chosen in a way that makes it reasonable to regard them as representative of American teens and parents of American teens.
a. When asked if they check their online social networking sites more than 10 times a day, 220 of the teens surveyed said yes. When parents of teens were asked if their teen checked his or her site more than 10 times a day, 40 said yes. Use a significance level of .01 to carry out a hypothesis test to determine if there is convincing evidence that the proportion of all parents who think their teen checks a social networking site more than 10 times a day is less than the proportion of all teens who report that they check more than 10 times a day.
b. The article also reported that 390 of the teens surveyed said they had posted something on their networking site that they later regretted. Would you use the two-sample z test of this section to test the hypothesis that more than one-third of all teens have posted something on a social networking site that they later regretted? Explain why or why not.
c. Using an appropriate test procedure, carry out a test of the hypothesis given in Part (b). Use = .05 for this test.