In an AP-AOL sports poll (Associated Press, December 18, 2005), 394 of 1000 randomly selected U.S. adults indicated that they considered themselves to be baseball fans. Of the 394 baseball fans, 272 stated that they thought the designated hitter rule should either be expanded to both baseball leagues or eliminated.
a. Construct a 95% confidence interval for the proportion of U.S. adults who consider themselves to be baseball fans.
b. Construct a 95% confidence interval for the proportion of those who consider themselves to be baseball fans who think the designated hitter rule should be expanded to both leagues or eliminated.
c. Explain why the confidence intervals of Parts (a) and (b) are not the same width even though they both have a confidence level of 95%.