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. Show all work and justify your answer.

Color Brown=80 Yellow=45 Orange=30 Green=30 Tan=15

(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

here null hypothesis:Ho: sample distirbution of colors follow  published color distribution

alternative hypothesis:Ha:at least one color does not follow published color distribution

applying chi square goodness of fit test:

chi square test statistic =11.429

for above degree of freedom =categories-1=5-1=4

for 4 df and above test statistic p vlaue =0.0221

as p value is less than 0.05 level we can reject null hypothesis and conclude that   published color distribution is notcorrect.

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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