In a poll of $472$ human resources directors, $63\%$ expressed the belief that they would be hiring new staff in the next three months. What is the $98\%$ confidence interval for the proportion of all personnel directors intending to hire personnel over the next three months?

Group of answer choices

$0\mathrm{.}63\backslash$pm $0\mathrm{.}057$

$0\mathrm{.}63\backslash$pm $0\mathrm{.}047$

$0\mathrm{.}63\backslash$pm $0\mathrm{.}052$

$0\mathrm{.}63\backslash$pm $0\mathrm{.}042$