Question

Common Sense Media surveyed 1,000 teens and 1,000 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. 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 checks his or her site more than 10 times a day, 40 said yes. The researchers used these data to conclude that there was 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 the sites more than 10 times a day.

Short answer

The researchers' conclusion is correct. The proportion of teenagers who reported checking their social networking sites more than 10 times a day (22%) is greater than the proportion of parents who believe their teen checks their social networking sites more than 10 times a day (4%).

Step-by-step solution

Calculate the Proportions

First, calculate the two proportions. For teens, the proportion is \(220/1000 = 0.22\) meaning 22% of teens reported frequently checking their social networking sites. Similarly for parents, the proportion is \(40/1000 = 0.04\) representing 4% of parents believe their child frequently checks their social sites.

Compare the Proportions

After calculating the two proportions, compare them. Here, the proportion of teens is 0.22 and the proportion of parents is 0.04. Thus, it can be observed that the proportion of teens reporting frequent use of social networking sites exceeds that of the parents' perception.

Conclude the Results

After the comparison, it becomes clear that the proportion of all parents who believe 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 their social sites more than 10 times a day. This aligns with the researchers' conclusion, meaning the researchers' conclusion was accurate.