In: Statistics and Probability
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.
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