Question: During the 2004 election year, new polling results were reported daily. In an IBD/TIPP poll of 910 adults. 503 respondents reported that they were optimistic about the national outlook, and President Bush's leadership index jumped 4.7 points to 55.3 ( Investor Busi-ness Daily. January 14. 2004).
a. What is the sample proportion of respondents who are optimistic about tlw. national outlook?
b. A campaign manager wants to claim that this poll indicates that the majority of adults are optimistic about the national outlook. Construct a hypothesis test so that rejection of the null hypothesis will permit the conclusion that the proportion optimistic is greater than 50%.
c. Use the polling data to compute the p-value for the hypothesis test in part (b). Explain to the manager what this p-value means about the level of significance of the results.