The costs associated with conducting interviews for a job opening have skyrocketed over the years. According to a Harris interactive survey, $260$ of $500$ senior human resources executives at U$.$S companies believe that their hiring managers are interviewing too many people to find qualified candidates for the job.

The $90\%$ confidence interval for the true proportion p of human resource executives who believe that their hiring managers are interviewing too many people, is given by

$0\mathrm{.}52\backslash$pm $0\mathrm{.}0491$

$0\mathrm{.}52\backslash$pm $0\mathrm{.}0367$

$0\mathrm{.}52\backslash$pm $0\mathrm{.}0523$

$0\mathrm{.}52\backslash$pm $0\mathrm{.}0862$