Answer
$0.152\lt\mu\lt0.274$
Work Step by Step
1. We have $\hat p=\frac{26}{122}=0.213, \hat q=1-\hat p=0.787 , n=122 $
2. At a 90% confidence the critical z-value is $z_{\alpha/2}=1.645 $
3. The margin of error can be found as
$E=z_{\alpha/2}\times\sqrt {\frac{\hat p\hat q}{n}}=1.645\times\sqrt {\frac{0.213\times0.787}{122}}=0.061$
4. Thus, the interval of the true proportion can be found as
$\hat p-E\lt p\lt\hat p+E$ which gives $0.152\lt\mu\lt0.274$
