Answer
The data does not support the obstetrician’s belief.
Work Step by Step
$H_0:~p=0.04$ versus $H_1:~p\lt0.04$
Requirement for a normal model:
$np_0(1-p_0)=120\times0.04(1-0.04)=4.608\lt10$
Since the requirement is violated, we do not use the normal model. Instead, a binomial model is appropriate.
$P(X\le3)\approx 0.29\gt 0.05$
Thus we do not reject the null hypothesis. There is not enough evidence to conclude that less than 4% of mothers smoke 21 or more cigarettes during pregnancy.
