Answer
$P$-value $\lt α$: null hypothesis is rejected.
There is enough evidence to conclude that the proportion of 20- to 24-year-olds who live on their own and do not have a land line is greater than 0.37.
Work Step by Step
$H_0:~p=0.37$ versus $H_1:~p\gt0.37$
$np(1-p)=30\times0.37(1-0.37)=6.993\lt10$
Test hypotheses with a small sample size:
$P$-value $=P(X\geq16)=1-P(X\lt16)=1-P(X\leq15)$
In order to find $P(X\leq15)$ use Excel: "=BINOMDIST(15;30;0.37;TRUE)"
$P$-value $=1-P(X\leq15)=1-0.9499=0.0501$
Since $P$-value $\lt α$, we reject the null hypothesis.
