Question

A random sample of 300 students from a geographic area indicated that 45 students attended private school. Estimate the true proportion of students attending private schools with 95% confidence

Answer 1

$n=300 \\ \hat{p}= \frac{45}{300}= 0.15 \\ α=1-0.95=0.05 \\ Z_{α/2}= 1.96 \\ CI= \hat{p}±Z \times \sqrt{ \frac{\hat{p}(1- \hat{p}}{n} } \\ CI = 0.15± 1.96 \times \sqrt{ \frac{0.15(1-0.15)}{300}} \\ = 0.15± 0.0404 \\ ( 0.1096 , 0.1904) \\ 0.1096<p<0.1904$