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