In a poll of 1000 randomly selected U.S. adults, 384 indicated that they considered themselves to be baseball fans. Of the 384 baseball fans, 292 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. (Round your answers to three decimal places.) (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. (Round your answers to three decimal places.) (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%. The widths of the confidence intervals are different because the sample sizes were different and because the sample proportions were different. The widths of the confidence intervals are different because the sample size of 292 fans who thought the designated hitter rule should be expanded is more than 50% the population size of 384 baseball fans. The widths of the confidence intervals are different because the sample size of 384 baseball fans is less than 50% of the population size of 1000 randomly selected U.S. adults. The widths of the confidence intervals are different because the z critical values used to calculate the confidence intervals are different.