Which candidate will win the upcoming presidential election? A survey of 1,300 likely voters found that 652 planned to vote for Candidate A, 600 planned to vote for Candidate \(\mathrm{B}\), and the rest were undecided.

a. Find and interpret a \(99 \%\) confidence interval for the difference in the population proportion of voters who will vote for either Candidate A or Candidate B.

b. Is there a significant difference between the proportion of voters who will vote for either Candidate A or Candidate B?

c. How big of a sample would be needed to find at least a \(5 \%\) difference?

d. What is the minimum proportion difference that a sample of size 1,300 would be able to find (provided such a difference were to exist)?