The Nellie Mae organization conducts an extensive annual study of credit card usage by college students. For their 2004 study, they analyzed credit bureau data for a random sample of 1,413 undergraduate students between the ages of 18 and 24. They found that 76% of the students sampled held a credit card. Three years earlier they had found that 83% of undergraduates sampled held a credit card. (Assume that the sample size was similar in 2001.)
a. State the appropriate null and alternative hypotheses for testing whether the proportion of undergraduate students who held a credit card differed between these two years.
b. Conduct an appropriate test of these hypotheses. Report the test statistic and p-value and summarize your conclusion.