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.

Color

Brown

Yellow

Orange

Green

Tan

Number

80

45

30

30

15

Identify the null hypothesis and the alternative hypothesis.

Determine the test statistic

Determine the P-value.

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

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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