DECIDE FOR YOURSELF DECIDING ABOUT ELECTIONS In the first week of November during an election year, you are very likely to hear the following statement on TV news, "We are now able to make a projection. In (insert the name of the state where you live), we project that the winner will be (insert one of the elected officials from your state)." Many people are aware that news agen- cies conduct exit polls on election day. A commonly asked question is, "How can an agency call a race based on the results from a sam- ple of only 1200 voters or so, and do this with a high (although not perfect) accuracy level?" Although the actual methods used to make projections based on exit polls are above the level of this book, we will examine a similar but simpler version of the question here. The con- cepts and logic involved in this process will help you understand the statistical inference concepts discussed in subsequent chapters. Consider a simple election where there are only two candidates, named A and B. Suppose p and q are the proportions of votes received by candidates A and B, respectively. Suppose we conduct an exit poll based on a simple random sample of 800 voters and determine the mean, standard deviation, and shape of the sampling distribution of p, where p is the proportion of voters in the sample who voted for candidate A. 1. Suppose that 440 of the 800 voters included in the exit poll voted for candidate A, which gives p = .55. Assuming that each candidate received 50% of the votes (i.e., p.50 and q .50, where p and q are the proportions of votes received by candidates A and B, respec- tively), what is the probability that at least 440 out of 800 voters in a sample would vote for candidate A? 2. Based on your answer to the above question, the results of the poll make it reasonable to conclude that the proportion of all voters who voted for candidate A is actually higher than .5. Explain why. 3. What implications do the above answers have for the result of the election? Will you make a projection about this election based on the results of this exit poll?