Answer
$X^2\lt X_α^2$: null hypothesis is not rejected.
There is not enough evidence to conclude that mothers between the ages of 35 and 39 years give birth to a higher percentage of low-birth-weight babies.
Work Step by Step
$H_0:~p=0.071$ versus $H_1:~p\gt0.071$
Total: 240 births
From item (a):
$E(low~birth~weight~babies)=17.04$
$E(not~low~birth~weight~babies)=222.96$
Observed number of low birth weight babies: 22
Observed number of not low birth weight babies: $240-22=218$
$X^2=Σ\frac{(O_i-E_i)^2}{E_1}=\frac{(22-17.04)^2}{17.04}+\frac{(218-222.96)^2}{222.96}=1.55$
$k=2$. So, $d.f.=2-1=1$
$X_α^2=X_{0.05}^2=3.841$
(According to Table VII, for d.f. = 1 and area to the right of critical value = 0.05)
Since $X^2\lt X_α^2$, we do not reject the null hypothesis.
