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In: Statistics and Probability

The color distribution of plain M&M’s varies by the factory in which they were made. The...

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 11 28 20 9 20 12

(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 α. 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.

Solutions

Expert Solution

a) here we can use chi square goodness of fit test for checking if Hackettstown factory color distribution is correct. we can use this as expected frequency for each category np >=5

b)

null hypothesis Ho: Sampling distribution of colors follows Hackettstown factory color distribution

alternative hypothesis: Ha:Sampling distribution of colors does not follows Hackettstown factory color distribution

c)

applying test:

observed Expected Chi square
category Probability(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei
red 0.125 11.000 12.500 0.180
orange 0.250 28.000 25.000 0.360
yellow 0.125 20.000 12.500 4.500
green 0.125 9.000 12.500 0.980
blue 0.250 20.000 25.000 1.000
brown 0.125 12.000 12.500 0.020
total 1.000 100 100 7.040

test statistic =7.040

d)

for above test statistic ; p value =0.22

e)

as p value is not less than 0.05 level ; we fail to reject Ho

f)as we reject null hypotheiss

we do not have evidence to reject  the claim that the Hackettstown factory color distribution is correct

orchestra answered 2 years ago
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