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Exploring M&M Color Distributions and Statistical Significance in a Classroom Setting

Engage students in a hands-on activity to analyze M&M color distributions through random sampling. Evaluate differences in individual and group results and draw conclusions on generalizing from samples. Learn about statistical significance and its importance in research. Practice applying terms like random selection, random assignment, and representative samples to the M&M study.

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Exploring M&M Color Distributions and Statistical Significance in a Classroom Setting

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  1. Do Now: Take out your HW & Work on your Level-Up Quizzes

  2. M&Ms Statistics • You have been given a “random sample” of M&Ms from the “population” of all M&Ms. • Open your package and complete your chart. DO NOT eat your M&Ms yet as this will interfere with your sample and invalidate your results.

  3. M&Ms Statistics • Based on your results, what would you expect the color distribution of M&Ms to be in a typical bag of M&Ms? • Now, form a group of 4-6 students, and re-calculate your distributions based on your combined sample. What happens with your results?

  4. M&Ms Distribution • For the last few years I have not been able to find accurate distributions on the Mars website. • Here is the most accurate info I could find: • As of 2008, a book cites these numbers: • Blue – 24% • Orange – 20% • Green – 16% • Yellow – 14% • Brown – 13% • Red – 13% • I also found a site that claimed the distribution was even (20% for each color)

  5. Conclusions about Samples • (Last Question on WKST) • Based on this exercise, what conclusions can you draw about generalizing results from a sample?

  6. M&Ms Statistics Now, imagine that you are testing the statement “M&Ms melt in your mouth but not in your hand.” Answer the questions on your wkst with a partner.

  7. M&Ms Statistics • Random Selection, Random Assignment, and Representative Sample • Apply these terms to the M&Ms study you have described.

  8. Making InferencesWhen Is an Observed Difference Reliable? • Representative samples are better than biased samples • Less-variable observations are more reliable than those that are more variable • More cases are better than fewer

  9. Making InferencesWhen Is a Difference Significant? • Statistical significance • The averages are reliable • The differences between averages is relatively large • Does imply the importance of the results

  10. Statistical Significance = a statistical statement of how likely it is that an obtained result occurred by chance. Represented by a p-value. The p-value is a statistical measure that tells how likely it is that the results were due to chance. Researchers need a p-value that is less than .05 to consider their results statistically significant.

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