Question: An a Pew Research survey from July 2009, participants were asked about the economic news that they had heard since May 2009. Forty-five percent of Independents stated that the news was mostly bad, as opposed to 48% of Republicans and 30% of Democrats. The study mentioned a total sample size of 1001. Assume that this sample included 395, 286, and 320 Independents, Republicans, and Democrats, respectively.
a. Construct a 95% confidence interval for the difference in the population proportions for each of the three pairs of political affiliations.
b. At the 1% level, can you conclude that the percentage of Independents who stated that the news was mostly bad was significantly different from the corresponding percentage of Republicans? Use the critical value method.
c. Repeat part b using the p-value method.