number of sample with confidence interval can be found with the formula;
[tex]n=pq(\frac{z_{\frac{\alpha}{2}}}{E})^2[/tex]Given the parameters;
[tex]\begin{gathered} p=16\text{ \%=0.16} \\ q=1-p=1-0.16=0.84 \\ z_{\frac{\alpha}{2}}=1.96 \\ E=4\text{ \%= 0.04} \end{gathered}[/tex]Thus, we have;
[tex]\begin{gathered} n=(0.16)(0.84)(\frac{1.96}{0.04})^2 \\ n=322.6944 \\ n\approx323 \end{gathered}[/tex]The number of sample needed to estimate the true proportion of children with good diets is 323
