Answer
$0.125\lt p\lt0.375$
No, it is in the above interval.
Work Step by Step
We have $\hat p=0.25, \hat q=1-\hat p=0.75 , n=80 $
At a 99% confidence the critical z-value is $z_{\alpha/2}=2.575 $
The margin of error can be found as
$E=z_{\alpha/2}\times\sqrt {\frac{\hat p\hat q}{n}}=2.575\times\sqrt {\frac{0.25\times0.75}{80}}=0.125$
Thus, the interval of the true proportion can be found as
$\hat p-E\lt p\lt\hat p+E$ which gives $0.125\lt p\lt0.375$
A proportion of families equal to 28% would not be considered large because it is in the above interval.
