Refer to Exercise 8.55. In the March opinion poll, suppose that 451 adults identified themselves as baseball fans, while the other 550 were not fans. The following question was posed:

Should major league baseball players be tested for steroids or other performance enhancing drugs, or not? Suppose that 410 of the baseball fans and 505 of those who are not fans answered yes to this question.

a. Construct a 95% confidence interval for the difference in the proportion of adults (fans versus nonfans) who favor mandatory drug testing for professional baseball players.

b. Does the data indicate that there is a difference in the proportion of fans versus nonfans who favor mandatory drug testing for professional baseball players? Explain.