A November 2011 Pew Research Center poll asked American social media users about their use of social media (such as Facebook, Twitter, MySpace, or LinkedIn). The study is based on a national telephone survey of 2277 adult social media users conducted from April 26 to May 22, 2011(www.pewinternet.org/Reports/2011/Why-Americans-Use-Social-Media/Main-report.aspx). According to this survey, 16% of 30- to 49-year-old and 18% of 50- to 64-year-old social media users cited connecting with others with common hobbies or interests as a major reason for using social networking sites. Suppose that this survey included 562 social media users in the 30 to 49 age group and 624 in the 50 to 64 age group.
a. Let p1 and p2 be the proportions of all social media users in the age groups 30 to 49 years and 50 to 64 years, respectively, who will cite connecting with others with common hobbies or interests as a major reason for using social networking sites. Construct a 95% confidence interval for p1 p2.
b. Using a 1% significance level, can you conclude that p1 is different from p2? Use both the critical-value and the p-value approaches.