Question

Consider the observed frequency distribution for the accompanying set of random variables. Perform a​ chi-square test using α = 0.05 to determine if the observed frequencies follow the Poisson probability distribution when lambda λ=1.5.

Random Variable, x Frequency, fo

   0    18

1 35

2 30

3 14

4 and more    3

Total    100

What is the null​ hypothesis, H0​?

A. The random variable follows a normal distribution.

B. The random variable does not follow the Poisson distribution with lambda λ=1.5.

C. The random variable follows a uniform distribution.

D. The random variable follows the Poisson distribution with lambda λ=1.5.

What is the alternate​ hypothesis, H1​?

A. The random variable follows a uniform distribution.

B. The random variable follows the Poisson distribution with lambda λ=1.5.

C. The random variable does not follow the Poisson distribution with lambda λ=1.5.

D. The random variable follows a normal distribution.

Calculate the test statistic.

χ2= ​(Round to two decimal places as​ needed.)

Determine the​ p-value.

​p-value=​(Round to three decimal places as​ needed.)

State the appropriate conclusion.

(Do not reject/Reject) the null hypothesis because the​ p-value is (greater than/less than) alpha α. There is (sufficient/insufficient) evidence to conclude that the observed frequency distribution does not follow Poisson probability distribution. Click to select your answer(s).

Answer 1