The UMUC Daily News reported that the color distribution for plain M&M’s was: 35

Question

The UMUC Daily News reported that the color distribution for plain M&M’s was: 35% brown, 30% yellow, 15% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 200 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.

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

(b) Determine the test statistic. Show all work;

(c) Determine the P-value. Show all work

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

color Brown Yellow Orange Green Tan Number 80 45 30 30 15

Explanation / Answer

a) null hypothesis: Ho: published color distribution is correct

alternative hypothesis:Ha:at least one proportion of color is different from published color distribution

b)applying chi square goodness of fit test:

fom abve test statistic =11.429

c) degree of freedom =categories-1=5-1=4

for 4 df and above test statistic p value =0.0221

d)as p value is less than 0.05 level we reject null hypothesis,

observed Expected Chi square category Probability O E=total*p =(O-E)^2/E Brown 0.350 80.000 70.00 1.43 Yellow 0.300 45.000 60.00 3.75 Orange 0.150 30.000 30.00 0.00 Green 0.100 30.000 20.00 5.00 Tan 0.100 15.000 20.00 1.25 1 200 200 11.429

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