A study suggests that about
\[80\%\] of undergraduate students are working at a job. Researchers plan to do a follow-up study with a new sample of students. They'll use the new data to make a one-sample
\[z\] interval to estimate the proportion of students who are working at a job. The researchers plan on using a confidence level of
\[90\%\], and they want the margin of error to be no more than
\[\pm 1\%\].
If we assume
\[\hat p=0.80\], what is the smallest sample size required to obtain the desired margin of error?