Answer
$X^2\lt X_α^2$: the null hypothesis is not rejected.
There is not enough evidence to conclude that the distribution for the number of rocket hits can not be modeled by a Poisson random variable.
Work Step by Step
$H_0:$ the distribution for the number of rocket hits can be modeled by a Poisson random variable.
$H_1:$ the distribution for the number of rocket hits can not be modeled by a Poisson random variable.
Total: 576 rockets
$E(0)=226.7136$
$E(1)=211.3926$
$E(2)=98.5536$
$E(3)=30.6432$
$E(4~or~more~hits)=8.6976$
$X^2=Σ\frac{(O_i-E_i)^2}{E_i}=\frac{(229-226.7136)^2}{226.7136}+\frac{(211-211.3926)^2}{211.3926}+\frac{(93-98.5536)^2}{98.5536}+\frac{(35-30.6432)^2}{30.6432}+\frac{(8-8.6976)^2}{8.6976}=1.012$
$k=5$. So, $d.f.=5-1=4$
$X_α^2=X_{0.05}^2=9.488$
(According to Table VII, for d.f. = 4 and area to the right of critical value = 0.05)
Since $X^2\lt X_α^2$, we do not reject the null hypothesis.
