Answer
$0.407\leq p\leq0.433$
Work Step by Step
Given $n=1500, \hat p=0.42, c=0.95$
we have $\hat q=0.58, Z_{\alpha/2}=1.96$
The margin of error $E=1.96\times\sqrt \frac{0.42\times0.58}{1500}=0.013$
The confidence interval is $(0.42-0.013, 0.42+0.013)$
The true proportion of all adults who favor visiting historical sites for vacations is $0.407\leq p\leq0.433$
