According to a survey of 1,000 adult Americans conducted by Opinion Research Corporation, 210 of those surveyed said playing the lottery would be the most practical way for them to accumulate $ 200,000 in net wealth in their lifetime (“One in Five Believe Path to Riches Is the Lottery,” San Luis Obispo Tribune, January 11, 2006). Although the article does not describe how the sample was selected, for purposes of this exercise, assume that the sample is a random sample of adult Americans. Suppose that you want to use the data from this survey to decide if there is convincing evidence that more than 20% of adult Americans believe that playing the lottery is the best strategy for accumulating $ 200,000 in net wealth.
a. What hypotheses should be tested in order to answer this question?
b. The P-value for this test is 0.215. What conclusion would you reach if α = 0.05?