m&m paper

To state it simply, I am a true and proud chocoholic (choc•o•hol•ic; noun:a person who is excessively fond of chocolate). Quite often, I find myself in need of snacks, chocolate, cupcakes, and among all the junk food I eat M&M is my favorite candy to buy. Growing up, I always wonder why the different colors in the M&M bags were not equally distributed. Common sense tells me mass production of the different colored shells are made and then combined along the way before being distributed in their individual bags only to meet a certain weight requirement. According to the M&M’s website, any package of milk chocolate M&M’s should be distributed as such: 24% blue, 13% brown, 16% green, 20% orange, 13% red, and 14% yellow M&M's (Proportions found at http://www.m-ms.com/us/about/products/milkchocolate/). I wanted to test the proportions stated on the M&M’s website and see if they held true to a 14 oz. (396.9 gram) bag of milk chocolate M&M’s. Also, I wanted to compare the raw results to see how they compared to a uniform estimation (i.e. E(color) = 1/6). In order to analyze the qualitative variables, the one-sample test and chi-sqare (goodness-of-fit) test will be used.
Data
For this analysis project, a 14 ounce (396.3 gram) bag of M&M’s was used to obtain the raw data (observed quantities). The different colored M&M’s were separated into different bowls by color and counted to obtain their individual quantities. I counted all colors three times to reduce error in my analysis. Next, the total was obtained by adding all of the individual quantities of the different colors. The sample size was very large with n=442 individual M&M’s. The observed quantities,