The Color Distribution/Proportion of Peanut M&M’s
Determined by Chi Square Goodness of Fitness Test for a Multinomial Population

Table of Contents

Abstract……………….…………..…………………………………………….......3

Introduction………………………………………………………………………...3

Methodology…………………………………………………………………..……3

Results…….…………………………………………………………………..……5

Limitations……………………………………………………………….………....6

Conclusion…....…………………………………………………..………………...6

References……….…....…………………………………………………………....7

Abstract
The intent of this research paper is to determine whether the color distribution/proportion of peanut M&M’s derived from a random sample 14-ounce bag (o) is a good fit to the hypothesized distribution/proportion of an infinite population of peanut M&M’s as cited by Mars, Inc. (p).
Introduction
A 14-ounce bag of peanut M&M’s was utilized to observe and obtain the random sample color distribution/proportion data. According to Mars, Inc. and as shown on Table 1, p has hypothesized distribution/proportions of: Blue-0.23, Brown-0.12, Green-0.15, Orange-0.23, Red-0.12 and Yellow-0.15.
Table 1 – Color Distribution/Proportion Figures via Mars, Inc.
Color Milk
Chocolate Peanut Crispy Minis Peanut
Butter Almond
Blue 24% 23% 17% 25% 20% 20%
Brown 13% 12% 17% 13% 10% 10%
Green 16% 15% 16% 12% 20% 20%
Orange 20% 23% 16% 25% 20% 20%
Red 13% 12% 17% 12% 10% 10%
Yellow 14% 15% 17% 13% 20% 20%

Methodology Using a goodness of fit test for the distribution of a multinomial (more than two categories) population, this study will determine whether the color distribution/proportion of peanut M&M’s derived from a random sample (14-ounce bag) is a good fit with the hypothesized distribution/proportion of an infinite population of peanut M&M’s as cited by Mars, Inc. The null hypothesis (Hₒ) or the hypothesis this paper