Question

A survey is taken of males in a large state University using a SRS. 72% of the 100 males reported that college was easier than high school. Create a 95% confidence interval for the true percentage of males at the University who feel college is easier than high school.

Answer 1

$Standard\,error=\sqrt{\frac{p×(1-p)}{n}}=\sqrt{\frac{0.72×0.28}{100}}=0.045$

$z-value\,for\,95\%\,confidence=1.96$

$Upper\,bound=p+z×SE=0.72+1.96×0.045=0.808$

$Lower\,bound=p-z×SE=0.72-1.96×0.045=0.632$

Answer: 72%±4.5%