Discussion of The Study

 

Weaknesses:

While conducting the study, we determined several weaknesses to the study that may have influenced the data. First, the Mars Company may have changed the M&M proportions from the last time they were published. If so, our predicted proportions for each color would have been incorrect, causing the inference statistics to be invalid. Furthermore, the M&Ms were purchased from the same store but from two different boxes. Consequently, the packaging machine at the factory may have been on a run for a certain color, making the actual proportion appear more than the true proportion. A store would most likely order all the boxes of M&Ms together, so that they could also have similar proportions that are different from the true proportion. A packaging machine could have been malfunctioning or in need of calibration during the time that the purchased bags were being filled, this would change the proportion in the bags from the true proportion.

Extrapolation:

Our sample is large enough to allow for reasonable extrapolation of our results. For the Chi-Square Goodness-of-Fit test, each of our expected M&M counts per bag were greater than 5. For the hypothesis tests of proportions, the total number of each color multiplied by its mean proportion per bag was greater than 30.

 

The collected data could be extrapolated for the time period during which the expected M&M proportions were the same. After the Mars Company adjusts the proportions for each color, the results are not applicable. Often times, M&M proportions are readjusted after the Mars Company administers a survey to customers. These satisfaction surveys are taken periodically to ensure that customers are pleased with the color distribution. For example, if the Mars Company determines that green M&Ms are more attractive to the human eye than the other colors, it will increase the proportion of green M&Ms in a package.

 

Suggestions for Futher Studies:

 

This study could be extended by periodically sampling M&Ms from a single store to determine how often the proportions for each color change. Also, this study could be administered in numerous stores in various states to determine if the proportions of each color vary by store and/or geographical location. If this study is continued, more exact proportions for each color in a package could be determined. The Milk Chocolate M&Ms are made in two plants located in Cleveland, TN and Hackettsville, NJ. Samples could be taken from multiple plants to determine if the proportions differ at each manufacturing plant.