“Most Like It Hot” is the title of a press release issued by the Pew Research Center (March 18, 2009, www.pewsocialtrends.org). The press release states that “by an overwhelming margin, Americans want to live in a sunny place.” This statement is based on data from a nationally representative sample of 2,260 adult Americans. Of those surveyed, 1,288 indicated that they would prefer to live in a hot climate rather than a cold climate. Suppose that you want to determine if there is convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate.
a. What hypotheses should be tested in order to answer this question?
b. The P-value for this test is 0.000001. What conclusion would you reach if α = 0.01?