Question

A chocolate cookie producer claims that its cookies average 3 chips and that the distribution follows a Poisson distribution. A consumer group wanted to test this claim and randomly sampled 150 cookies. The resulting frequency distribution is shown below. At the 0.10 significance level, answer only the questions stated below regarding whether the population of x = the number of chips per cookie could be Poisson distributed with λ = 3.0. You will still be using aspects of the standard 5-step hypothesis testing procedure.

Chips

Per Poisson

Cookie Frequency Probabilites E = nπ __ ____

   0 0

   1 16

   2 38

   3 56

   4 27

   5 or more 13

   n = 150

(a) State the null and alternative hypotheses.

H₀:

H₁:

(b) What are the degrees of freedom?

(c) What is the Poisson Probability that the number of chips per cookie is exactly 1?

(d) What is the expected number of cookies from this sample that will have exactly two chips?

(e) State the decision rule.

(f) The calculated test value is equal to 32.7465 ; (1) What conclusion can be drawn from the information presented?;

(2) Provide a common sense statement given your conclusion.

Answer 1

Chips per Cookie	Frequency	Poisson Probabilities	E
0	0	0.049787068	7.46806
1	16	0.149361205	22.40418
2	38	0.224041808	33.60627
3	56	0.224041808	33.60627
4	27	0.168031356	25.2047
5 or more	13	0.184736755	27.71051

The hypothesis being tested is:

H0: The data follows a Poisson distribution

Ha: The data does not follow a Poisson distribution

P(x = 1) = 0.149361205

E(x = 2) = 33.60627

Reject Ho if p-value < 0.10

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