Peter Szeltner, Shubham Mangla, Zac Novak

 

 

  The Purpose of this Study:

The purpose of this study is to determine whether the proportion of M&M colors in a 1.69 oz bag significantly differ from each other. We decided to choose this study because we were interested in whether M&M colors were evenly proportioned in a bag. We also picked this topic because we wanted to confirm or reject previous studies on M&M proportions. We hypothesize that the proportions of colors will not be the same for each color, and we hope to show that they are different. To further our study, we are comparing individual color proportions to determine which ones are greater.

Abstract

 

Overview of The Study

We started our study by looking for similar studies conducted in the past using the search engine Google. By typing “M&M proportion studies” into Google, we found several different studies that tested the proportions of M&Ms to those stated by the M&M Company. We were able to make use of these previous studies as a base for our own study. Then, we obtained our sample, 80 1.69 oz. bags of M&Ms from Gordan’s Food Service, which contained a total of 4436 M&Ms. Our population of interest was all M&Ms made after the proportions from the company were last adjusted. After obtaining the 80 bags, we counted each bag individually and noted the number of M&Ms of each color in each bag. Then, we inserted our data into Minitab and calculated the proportion of each color in each bag. Next, we ran our four tests comparing individual proportions. In the first test, we wanted to determine whether the proportion of blue M&Ms in a bag is greater than the proportion of orange M&Ms in a bag. In the second test, we wanted to determine whether the proportion of red M&Ms in a bag is less than the proportion of blue M&Ms in a bag. In our third test, we wanted to determine whether the proportion of brown M&Ms in a bag is different than the proportion of green M&Ms in a bag. In our final test, we carried out a Chi-Square test to determine whether the proportions reported by the Mars Company differ from the actual propotions. After performing each test, we concluded that the true proportion of blue M&Ms is not significantly greater than the true proportion of orange M&Ms per bag, that the true proportion of red M&Ms is significantly less than the true proportion of blue M&Ms per bag, that the true proportion of green M&Ms is significantly different than the true proportion of brown M&Ms per bag, and that at least one of the proportions significantly differs from the proportions stated by the M&M company. Also, the graphs of each color's proportion per bag were approximately normally distributed. While performing the study, we found some weaknesses such as the fact that the proportions for each color may have been readjusted over time and that the bags came from two different boxes. Lastly, we concluded that our data can be extrapolated for the time period during which the proportions were the same.