13. The color distribution of plain M&M’s varies by the factory in which they we
ID: 2948178 • Letter: 1
Question
13. The color distribution of plain M&M’s varies by the factory in which they were made. The Hackettstown, New Jersey plant uses the following color distribution for plain M&M’s: 12.5% red, 25% orange, 12.5% yellow, 12.5% green, 25% blue, and 12.5% brown. Each piece of candy in a random sample of 100 plain M&M’s from the Hackettstown factory was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the Hackettstown factory color distribution is correct. Describe method used for calculating answer.
Color
Red
Orange
Yellow
Green
Blue
Brown
Number
9
27
11
14
22
17
(a) Identify the appropriate hypothesis test and explain the reasons why it is appropriate for analyzing this data.
(b) Identify the null hypothesis and the alternative hypothesis.
(c) Determine the test statistic. (Round your answer to two decimal places)
(d) Determine the p-value. (Round your answer to two decimal places)
(e) Compare p-value and significance level ?. What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why?
(f) Is there sufficient evidence to support the claim that the Hackettstown factory color distribution is correct? Justify your answer.
Color
Red
Orange
Yellow
Green
Blue
Brown
Number
9
27
11
14
22
17
Explanation / Answer
a) here as sample taken is random therefore it represents populaiton ; hence it is appropriate for analyzing this data.
we can use chi square goodness of fit test to see if Hackettstown factory color distribution is correct
b)
null hypothesis:Ho:Hackettstown factory color distribution is correct
alternate hypothesis:Ha:not all colors have similar distribution as stated by Hackettstown factory
c)
applying chi square goodness of fit test:
test statsitic =3.48
d)
for (categories-1=6-1 =5) degree if freedom and above test statistic p value =0.63
e)as p vlaue is not less than 0.05 level of significance we fail to reject null hypothesis
f)as we fail to reject null hypothesis
we do not have sufficient evidence to rject the claim that the Hackettstown factory color distribution is correct
observed Expected Chi square category Probability(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei Red 0.125 9.000 12.500 0.980 Orange 0.250 27.000 25.000 0.160 Yellow 0.125 11.000 12.500 0.180 green 0.125 14.000 12.500 0.180 Blue 0.250 22.000 25.000 0.360 Brown 0.125 17.000 12.500 1.620 total 1.000 100 100 3.480Related Questions
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