Chapter 9, Problem 71CP

Brown or Whitman? California’s governor election in 2010 had two major candidates, Brown and Whitman.

1. a. For a random sample of 650 voters in one exit poll, 360 voted for Brown, 240 for Whitman, and the rest for someone else. Conduct all five steps of a test of H₀: p = 0.50 against H_a: p ≠ 0.50, where p denotes the probability that a randomly selected voter prefers Brown. Would you be willing to predict the outcome of the election? Explain how to make a decision, using a significance level of 0.05.
2. b. Suppose the sample size had been 50 voters, of whom 28 voted for Brown. Show that the sample proportion is similar to the sample proportion in part a, but the test statistic and P-value are very different. Are you now willing to predict the outcome of the election?
3. c. Using part a and part b, explain how results of a significance test can depend on the sample size.