EXAMPLE 5.11 Social Media Purchasing Influence

Although many companies run aggressive marketing campaigns on social media, a Gallup survey reveals that 62% of all U.S. respondents say Twitter and Facebook, among other sites, do not have any influence on their decisions to purchase products.⁵ It was also reported, however, that baby boomers were less likely to be influenced than younger respondents. You decide to take a nationwide random sample of 2500 college students and ask if they agree or disagree that “Social media advertising influences my purchasing decisions.” Suppose that it were the case that 45% of all college students would disagree if asked this question. In other words, 45% of all college students feel that social media has no influence on their purchasing decisions. What is the probability that the sample proportion who feel that social media has no influence is no greater than 47%?

The count of college students who feel no influence has the binomial distribution . The sample proportion does not have a binomial distribution because it is not a count. But we can translate any question about a sample proportion into a question about the count . Because 47% of 2500 is 1175,

This is a rather tedious calculation. We must add 1176 binomial probabilities. Software tells us that . But what do we do if we don’t have access to software?