The UMUC Daily News reported that the color distribution for plain M&M’s was: 40

Question

The UMUC Daily News reported that the color distribution for plain M&M’s was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M’s was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct. Show all work and justify your answer.

Color

Brown 35

Yellow 25

Orange 16

Green 10

Tan 14

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the claim that the published color distribution is correct? Justify your answer.

Explanation / Answer

(a) H0:there is sufficient evidence to support the claim that the published color distribution is correct

H1: :there is not sufficient evidence to support the claim that the published color distribution is correct

Let the los be alpha = 5%

(b) From the given data

Num Categories: 5
Degrees of freedom: 4

Test Statistic, X^2: 4.2750
Critical X^2: 9.48772
c) P-Value: 0.3701

Here P-value > alpha 0.05, so we accept H0

(d) we conclude that there is sufficient evidence to support the claim that the published color distribution is correct i.e. claim is valid

Observed Expected Color Freq (Oi) Probability Freq Ei (Oi-Ei)^2 /Ei Brown 35 0.40 40 0.625 Yellow 25 0.20 20 1.25 Orange 16 0.20 20 0.8 Green 10 0.10 10 0 Tan 14 0.10 10 1.6 Total: 100 100 4.275

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