The sample proportion, p, would be
p = 78 ÷ 124 = 0.63
To find the true population proportion, P, the equation would be
[tex]p+z( \sqrt{ \frac{p(1-p)}{n} } ) \ \ \textless \ P\ \textless \ p-z( \sqrt{ \frac{p(1-p)}{n} } )[/tex]
where n = 124, and z = 1.645 for a 90% confidence interval
Substituting,
[tex]0.63+1.645( \sqrt{ \frac{0.63(1-0.63)}{124} } ) \ \ \textless \ P\ \textless \ 0.63-1.645( \sqrt{ \frac{0.63(1-0.63)}{124} } )[/tex]
[tex]0.7 \ \textless \ P\ \textless \ 0.56[/tex]
