In a book the characters are trying to determine whether the Poisson probabilistic model can be used to describe the locations that rockets landed in a city. They divided the city into
0.25-km² regions. They then counted the number of rockets that landed in each region, with the results shown in the table below. Complete parts (a) through (e).
Number of rocket hits
Observed number of regions
0
229
1
209
2
96
3
30
4
7
5
0
6
0
7
1
Let $p_0$, $p_1$, $p_2$, and $p_3$ be the probability that there are 0, 1, 2, and 3 rocket hits in a given region, and let $p_4$ be the probability that there are 4 or more. Choose the correct null and
alternative hypotheses below.
A. $H_0$: The rockets strikes can be modeled by a Poisson random variable.
$H_1$: The rocket strikes do not follow a Poisson distribution.
B. $H_0$: $p_1 = p_2 = p_3 = p_4$
$H_1$: $p_1 \neq p_2 \neq p_3 \neq p_4$
C. $H_0$: The rocket strikes do not follow a Poisson distribution.
$H_1$: The rockets strikes can be modeled by a Poisson random variable.
D. $H_0$: $p_1 \neq p_2 \neq p_3 \neq p_4$
$H_1$: $p_1 = p_2 = p_3 = p_4$
Compute the test statistic, $\chi_0^2$
$\chi_0^2 = $
(Round to three decimal places as needed.)
