The UMUC Daily News reported that the color distribution for plain M&M’s was: 40
ID: 3330582 • Letter: T
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
(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?
Color
Brown
Yellow
Orange
Green
Tan
Number
42
21
12
7
18
Color
Brown
Yellow
Orange
Green
Tan
Number
42
21
12
7
18
Explanation / Answer
null hypothesis: Ho: color distribution for plain M&M’s is 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan.
alternate hypothesis: Ha: above given colors distribution is not correct.
b) applying chi square goodness of fit test:
from above test statistic X2 =10.65
c) for degree of freedom =number of categories -1 =5-1=4
for 4 degree of freedom and abvoe test statisitc ; p value =0.0308
d) as p vlaue is less then 0.05 level we can reject null hypothesis
we have sufficient evidence to reject the claim that the published color distribution is correct
observed Expected Chi square Type Probability O E=total*p =(O-E)^2/E Brown 0.400 42.000 40.00 0.10 Yellow 0.200 21.000 20.00 0.05 Orange 0.200 12.000 20.00 3.20 Green 0.100 7.000 10.00 0.90 Tan 0.100 18.000 10.00 6.40 1 100 100 10.6500Related Questions
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