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The Distribution of M&M’s

The Distribution of M&M’s. Bryan Wu/ Hongbo Liu. Question: Does the actual distribution of Peanut M&M colors follow the proportions claimed by the manufacturer?.

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The Distribution of M&M’s

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  1. The Distribution of M&M’s Bryan Wu/ Hongbo Liu

  2. Question:Does the actual distribution of Peanut M&M colors follow the proportions claimed by the manufacturer? This following study was conducted for the purpose of an AP Statistic Class investigation. There is no guarantee on the validity on any or all parts of the study. The conductor(s) of the study take no responsibility in the accuracy of the results.

  3. Background Information • Small, sugar-coated, milk chocolate pieces, produced by Mars, Incorporated • Variations- milk chocolate, peanut, mint chocolate, dulce de leche, toffee, crispy, almond, peanut butter, white chocolate and dark chocolate. • Six colors: red, orange, yellow, green, brown, and blue

  4. Procedure ACME- 272 East Butler Avenue, Ambler, PA Numbered 8 bags from 1-8 Counted the number of M&M’s for each color randInt (1,8,1)=2

  5. 45 Data 25 22 19 168 30 27

  6. Using the Chi-Square Test for Goodness Fit Is there is a relationship between two categorical variables? Variables>Proportions from the sample we purchased >Proportions provided by the manufacturer

  7. Assumptions for Chi-Square • Simple Random Sample • -Yes; the sample was selected using random allocation • All individual expected values are at least 1 • -Yes • No more than 20% of the expected counts are less than 5 • -Yes; none are less than 5

  8. Hypotheses • Null Hypothesis: H0: The actual population proportions of M & M Colors are equal to the proportions claimed by the manufacturer • Alternative Hypothesis: Ha: The actual population proportions of M & M Colors are NOT equal to the proportions claimed by the manufacturer

  9. Red Blue Orange Green Brown Yellow Total Observed 25 27 45 22 30 19 168 Expected Expected proportions 20.16 38.64 38.64 25.2 20.16 25.2 168 0.12 0.23 0.23 0.15 0.12 0.15 1 Before conducting the test

  10. Observed (O) Expected (E) ((O-E)^2)/E 25 20.16 1.162 27 38.64 3.5065 45 38.64 1.0468 22 25.2 0.40635 30 20.16 4.8029 19 25.2 1.5254 Chi-Square Test for Goodness of Fit Formula X²= 1.162+3.5065+1.0468+.40635+4.8029+1.5254 = 12.4499 Test Statistic: X²=12.4499 Degrees of Freedom: n-1=5

  11. P-Value & Rejection of Null Hypothesis • P(X²≥X²)=.0291 • .0291<.05 • Reject the null hypothesis at 0.05 significance level

  12. Conclusion The actual population proportions of M & M Colors are NOT equal to the proportions claimed by the manufacturer. HOWEVER… • Larger sample chosen from more varied sources should be used. • Statisticians should repeat this investigation multiple times to evaluate the validity of the manufacture’s claims

  13. Future study • Examine color distributions from different locations • Conduct the same test on other flavors (almond, white chocolate, dark chocolate)

  14. SOURCES • http://en.wikipedia.org/wiki/M%26m%27s • http://us.mms.com/us/about/products/peanut

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