Answer
$P$-value $=0.00209$
Work Step by Step
$P$-value = $P(X\geq14)=1-P(X\lt14) =1-P(X \leq13)$
In order to find $P(X \leq13)$ use Excel: "=BINOMDIST(13;16;0.5;TRUE)"
$P$-value $=1-P(X \leq13)=1-0.99791=0.00209$
We reject the null hypotheses.
Notice that $P$-value$\lt0.01$, which is the smallest level of significance we have used.
