A poll is taken in which \(342\) out of \(500\) randomly selected voters indicated their preference for a certain candidate.

(a) Find a \(99\)% confidence interval for \(p\text{.}\)

\(\leq p \leq\)

(b) Find the margin of error for this \(99\)% confidence interval for \(p\text{.}\)

(c) Without doing any calculations, indicate whether the margin of error is larger or smaller or the same for an 80% confidence interval.