A November 2011 Gallup poll asked American adults about their views of healthcare and the healthcare system in the United States. Although feelings about the quality of healthcare were positive, the same cannot be said about the quality of the healthcare system. According to this study, 29% of Independents and 27% of Democrats rated the healthcare system as being excellent or good (www.gallup.com/poll/ 150788/Americans-Maintain-Negative-View-Healthcare-Coverage.aspx). Suppose that these results were based on samples of 1200 Independents and 1300 Democrats.
a. Let p1 and p2 be the proportions of all Independents and all Democrats, respectively, who will rate the healthcare system as being excellent or good. Construct a 97% 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.