Answer
$0.092\lt\mu\lt0.152$
$11\%$ is in the interval
Work Step by Step
1. We have $\hat p=\frac{55}{450}=0.122, \hat q=1-\hat p=0.878 , n=450 $
2. At a 95% confidence the critical z-value is $z_{\alpha/2}=1.96 $
3. The margin of error can be found as
$E=z_{\alpha/2}\times\sqrt {\frac{\hat p\hat q}{n}}=1.96\times\sqrt {\frac{0.122\times0.878}{450}}=0.030$
4. Thus, the interval of the true proportion can be found as
$\hat p-E\lt p\lt\hat p+E$ which gives $0.092\lt\mu\lt0.152$
5. Since $11\%=0.11$ is in the above range, the above range is a good estimate of the population proportion.
