In a book the character are trying to determine whether the Poisson probabilistic model can be used to describe the locations that rockets landed in city. They divided the city into 0.25km ² 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).

(a) Estimate the mean number of rocket hits in region by computing ? = ?x P(x) ? = ?

(b) Explain why the requirement for conducting a goodness-of-fit test are not satiffied.

A. More than 20% of the expected counts are less than 5.

B. The data are note categorical.

C. Not all expected counts are greater than 1.

D. The data are not normally distributed.

(c) After consolding the table, we obtain the following distribution for rocket hits. Using the passion probability model,

Where ? is the mean from part (a), we can obtain the probability distribution for the number of rocket hits. Find the probability of 0 hit in region. Then find probability of 1 hit, 2 hit, 3 hits and 4 more hits.

(d) A total of n = 575 rockets was fired. Determined the expected number of regions hit by computing ?expected number of regions? = np, where p is the probability of observing that particular number of hits in the region.

(e) Conduct a goodness-of-hit test for the distribution using the ? = 0.05 level of significance.

Do the rockets appear to be modeled by a Poisson random variable?

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 _o : p ₁ = p ₂ = p ₃ = p ₄

H ₁ : p ₁ ? p ₂ ? p ₃ ? p ₄

B. H _o : The rockets strikes can be modeled by a Poisson random variable.

H ₁ : The rockets strikes do not follow a Poisson distribution.

C. H _o : The rockets 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 ? p ₂ ? p ₃ ? p ₄

H _o1 : p ₁ = p ₂ = p ₃ = p ₄

Compute the test statistic ? ² ₀ . ? ² ₀ = ?

Obtain the P-value

P-value = ?

State the conclusion:

A. Do not reject H ₀ . There is insufficient evidence to reject the claim the rocket strikes can be modeled by a Poisson random variable.

B. Do not reject H ₀ . There is sufficient evidence to reject the claim that the rocket strikes can be modeled by a Poisson random variable.

C. Reject H ₀ . There is insufficient to reject the claim that the rocket strikes can be modeled by a Poisson random variable.

D. Reject H ₀ . There is sufficient evident to reject the claim that the rockets strikes can be modeled by a Poisson random variable.

Number of rocket hits Observed number of regions 0 221 1 215 2 98 3 32 4 8 50 60 7 1 P(x) = x! 1- Number of rocket hits Observed number of regions Probability 0 221 1 215 2 98 32 32 4 or more 9 Number of rocket hits Observed number of regions Expected number 0 221 1 215 ON 2 98 3 32 4 or more 9