Answer to Question #217935 in Statistics and Probability for Vickie

Question

Out of a sample of 80 students from a college 32 were female students determine the 95% confidence interval of the proportion of female Students in the population

Answer 1

$\hat{p}=\frac{32}{80}=0.4 \\ n=80$

The formula for a CI for a population proportion is

$\hat{p}±z \times \sqrt{ \frac{\hat{p}(1- \hat{p})}{n} }$

z=1.96 for 95 % confidence interval

CI:

$0.4 ±1.96 \times \sqrt{ \frac{0.4(1- 0.4)}{80} } \\ 0.4 ± 1.96 \times 0.05477 \\ 0.4 ±0.107 \\ (0.293, 0.507)$