In 2010, the National Football League adopted new rules designed to limit head injuries. In a survey conducted in 2015 by the Harris Poll, 1216 of 2096 adults indicated that they were football fans and followed professional football. Of those who were football fans, 692 said they thought that the new rules were effective in limiting head injuries.

a. If the sample is representative of adults in the United States, construct and interpret a 95% confidence interval for the proportion of U.S. adults who consider themselves to be football fans.

b. Construct and interpret a 95% confidence interval for the proportion of football fans who think that the new rules have been effective in limiting head injuries.

c. Explain why the confidence intervals in Parts (a) and (b) are not the same width even though they both have a confidence level of 95%.