Are you more likely to purchase a brand mentioned by an athlete on a social media site? According to a Catalyst Digital Fan Engagement survey, 53% of social media sports fans would make such a purchase.
a. Suppose that the survey had a sample size of n - 500. Construct a 95% confidence interval estimate for the population proportion of social media sports fans that would more likely purchase a brand mentioned by an athlete on a social media site.
b. Based on (a), can you claim that more than half of all social media sports fans would more likely purchase a brand mentioned by an athlete on a social media site?
c. Repeat parts (a) and (b), assuming that the survey had a sample size of n = 5,000.
d. Discuss the effect of sample size on confidence interval estimation.