Question: [14 marks] The Bowl Championship Series (BCS) was designed to select the top two teams in college football for a final championship game. The teams are selected by a complicated formula. In 2001, the University of Miami Hurricanes and the University of Nebraska Corn-huskers played for the championship. However, many football fans thought that Nebraska should not have played in the game because it was rated only fourth in both major opinion polls. Third-ranked University of Colorado fans were particularly upset because Colorado soundly beat the Cornhuskers late in the season.

A new CNN/USA Today/Gallup poll reports that a majority of fans would prefer a national championship play-off as an alternative to the BCS. The news media polled a random sample of 1019 adults 18 years of age or older. A summary of the results states that 54% prefer the play-off and the margin of error is 3% for 95% confidence level.

a. [4 marks] Give the 95% CI.

b. [6 marks] Interpret the CI obtained in part (a).

c. [4 marks] Do you think that a newspaper headline stating that a majority of fans prefer a play-off is justified by the results of this study? Explain your answer.