Question

In a graduate teacher college, a survey was conducted to determine the proportion of students who want to major in Mathematics. If 378 out of 900 students said Yes, with 95% confidence, what interpretation can we make regarding the probability that all students in the teacher graduate college want to major in Mathematics.

Answer 1

$\hat{p}=\frac{378}{900}=0.42\\Confidence\,\,interval:\\\left( \hat{p}-\sqrt{\frac{\hat{p}\left( 1-\hat{p} \right)}{n}}z_{\frac{1+\gamma}{2}},\hat{p}+\sqrt{\frac{\hat{p}\left( 1-\hat{p} \right)}{n}}z_{\frac{1+\gamma}{2}} \right) =\\=\left( 0.42-\sqrt{\frac{0.42\left( 1-0.42 \right)}{900}}\cdot 1.960,0.42+\sqrt{\frac{0.42\left( 1-0.42 \right)}{900}}\cdot 1.960 \right) =\\=\left( 0.387754,0.452246 \right)$