Answer
$0.721\lt p\lt0.819$
Work Step by Step
We have $\hat p=\frac{154}{200}=0.77, \hat q=1-\hat p=0.23 , n=200 $
At a 90% confidence the critical z-value is $z_{\alpha/2}=1.645 $
The margin of error can be found as
$E=z_{\alpha/2}\times\sqrt {\frac{\hat p\hat q}{n}}=1.645\times\sqrt {\frac{0.77\times0.23}{200}}=0.049$
Thus, the interval of the true proportion can be found as
$\hat p-E\lt p\lt\hat p+E$ which gives $0.721\lt p\lt0.819$
