Answer
$X^2\gt X_α^2$: the null hypothesis is rejected.
The distribution of weapon choice in robberies in schools does not follow the national distribution.
Work Step by Step
$H_0:$ the distribution of weapon choice in robberies in schools follows the national distribution
$H_1:$ the distribution of weapon choice in robberies in schools does not follow the national distribution
Total: 1652 robberies.
Expected count of Gun: $1652\times0.42=693.84$
Expected count of Knife: $1652\times0.09=148.68$
Expected count of Strong-arm: $1652\times0.40=660.8$
Expected count of Other: $1652\times0.09=148.68$
$X^2=Σ\frac{(O_i-E_i)^2}{E_1}=\frac{(329-693.84)^2}{693.84}+\frac{(122-148.68)^2}{148.68}+\frac{(857-660.8)^2}{660.8}+\frac{(344-148.68)^2}{148.68}=511.475$
$k=4$. So, $d.f.=4-1=3$
$X_α^2=X_{0.05}^2=7.815$
(According to Table VII, for d.f. = 3 and area to the right of critical value = 0.05)
Since $X^2\gt X_α^2$, we reject the null hypothesis.
