Practicum Example 5: Testing Mars Chocolate

[M&Ms]

Some M&Ms that I did not get from the vending machine because I have no change on me. Photo courtesy Mars Chocolate, China.

Let us escape the weather for a moment and examine corporate fraud. M&Ms are produced by Mars Chocolate N.A., LLC, which is located in Hackettstown, NJ. On their website, they state that the distribution of colors in their Milk Chocolate M&Ms follows the following probability distribution:

Table 1: Hypothesized probability distribution for each M&M color.
Color: Blue Orange Green Yellow Red Brown
Proportion: 0.24 0.20 0.16 0.14 0.13 0.13

I have no doubt that they are telling the truth. But, in the interest of finding a reason to legitimately eat chocolate, I wish to test the corporation’s claim using statistics.

Research Question: Is this stated distribution reasonable, or is there significant evidence that it is not the correct distribution of colors?

Collecting the Data

Here, you get to collect your own data. You will need to purchase some Milk Chocolate M&M candies. An important question is: How many should you purchase? While the final answer is yours to make, my experience suggests that you will need at least 12 ounces, but that 32 ounces will give better results. Whatever sample size you decide upon, make sure you discuss in your write-up what effect your decision had on your analysis.

Now that you have your Milk Chocolate M&M candies, you just need to open the bag(s) and create a frequency table for the six colors. That table will be all the information you need for this analysis.

Analyzing the Data

Use the data to answer the research question.

Interpreting the Results

Interpret your analysis. Include appropriate graphics. Make sure that you defend your choices in your analysis. Be explicit about what statistical procedures you ran and why you ran those procedures. Your reader (me) should not have to guess.

Do the above before looking at the solutions. Jumping straight to the solutions provides almost no help for you. The benefit from practice is actually doing the practice. Do not cheat yourself… especially because dong this practice results in chocolate!