The sample size in this problem is [tex]\(100\)[/tex] students.
Estimate the population proportion as [tex]\(\hat{p} = 0.5\)[/tex].
[tex]\[
(1 - \hat{p}) = 1 - 0.5 = 0.5
\][/tex]
When the margin of error is calculated using the formula [tex]\(E = z^{\star} \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}\)[/tex],
To the nearest tenth of a percent, the result is [tex]\(9.8\%\)[/tex].