(1) Is there any pure or mixed strategy equilibrium? If there are, what are they? (8%)

IV. (20%) Suppose, in a poll of 910 adults, 503 respondents reported that they were optimistic about the national outlook. The Press Secretary claims that this poll indicates that the majority of adults are optimistic about the nation's outlook. Conduct a hypothesis test using the p-value approach and use α = 0.05 for the level of significance to test the Press Secretary's statement.