Question

Upon request, the Mars Company (the maker of M&M's) will provide the color distribution for their candies. As of August 2009, they noted that

"Our color blends were selected by conducting consumer preference tests, which indicate the assortment of colors
that pleased the greatest number of people and created the most attractive overall effect.

On average, our mix of colors for M&M'S CHOCOLATE CANDIES is:

M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown."

Data collected from a bag of Milk Chocolate M&M's are provided.

Blue	Brown	Green	Orange	Red	Yellow
110	47	52	103	58	50

We want to determine if this sample provides evidence that the color distribution has changed since August 2009.

Reference: 7-10

Find the expected counts for each color using the sample size (420 total candies) and null hypothesis.

Answer 1

Ho: The null hypothesis states that the proportion of colors of M&M chocolate candies is same as 2009; i.e

Pblue= 0.24 , porange= 0.20, pgreen= 0.16, pyellow= 0.14, pred= 0.13, pbrown= 0.13

Ha: Some of the population proportions differ from the values stated in the null hypothesis

This corresponds to a Chi-Square test for Goodness of Fit.

Test statistics: Chi-Square test for Goodness of Fit.

Nos of die	Observed values (fo)	Expected Proportions	Expected values (fe)	(fo-fe)2/ fe
blue	110	0.240	100.80	0.840
brown	47	0.130	54.60	1.058
green	52	0.160	67.20	3.438
orange	103	0.200	84.00	4.298
red	58	0.130	54.60	0.212
yellow	50	0.140	58.80	1.317
Total	420	1.000	420.00	11.162

Expected values are the expected counts. (fe)