Answer
$P$-value $\gt α$: null hypothesis is not rejected.
There is not significant evidence to conclude that the proportion of adolescents who pray daily is greater than 0.4.
Work Step by Step
$H_0:~p=0.4$ versus $H_1:~p\gt0.4$
$np_0(1-p_0)=40\times0.4(1-0.4)=9.6\lt10$
Test hypotheses with a small sample size:
$P$-value $=P(X\geq18)=1-P(X\lt18)=1-P(X\leq17)$
In order to find $P(X\leq17)$ use Excel: "=BINOMDIST(17;40;0.4;TRUE)"
$P$-value $=1-P(X\leq17)=1-0.6885=0.3115$
Since $P$-value $\gt α$, we do not reject the null hypothesis.
