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Trail Mix Statistics

Trail Mix Statistics

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Trail Mix Statistics

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  1. Trail Mix Statistics By Tyler Lipshutz

  2. About Trail Mix • Made with dried fruits, grains, nuts, and sometimes chocolate • Ideal for long outdoor hikes • 1968 when first invented in California • GORP, “Good Old Raisins and Peanuts” • Planters • Emerald • Archer Farms • Third Party brands (Wegmans)

  3. My Goal: • Is the distribution in serving sizes equal to the entire bag? Does the bags overall weight distribute equal to the estimated amount of servings?

  4. How I collected my data • Two different trail mixes • Planters & Wegmans • $1.59/ 6 oz. & $4.69/ 16 oz. • Count the amount in each bag • Find the weight of the serving • Pick one random piece and count how many were in that serving. • Record data into charts

  5. Distribution of Pieces – Planters. • Peanuts (53%) • Raisins(24%) • M&Ms(17%) • Almonds(3%) • Cashews(3%)

  6. Distribution of Pieces – Rainbow Delight • Peanuts (59%) • Raisins(14%) • M&Ms(21%) • Almonds(3%) • Cashews(3%)

  7. Brand vs. Weight • Shape: • Both are roughly unimodal, P has two peaks around 34 g and 46 g with a gap at 36. RD has peaks at 32 g and 42 g and a gap at 43. • Center: Planters has a center at 34. 9 g. RD has a center at 36.0323 g. • Spread: Planters has a wider spread with a range of 41 and RD has a range of 27.

  8. Quantitative Data – Product vs. Peanuts • Shape: Planters is right skewed and RD is close to unimodal • Center: Planters mean is 17.2 and RD is 21.1667 • Spread: Planters has the greater spread with a range of 17 but Rainbow Delight has a range of 14. Planters has a stdDev of 7.4632 and Rainbow Delight has a stdDev of 5.1929.

  9. Quantitative Data – Product vs. M&Ms • Shape: Both are slightly unimodal • Center: Planters mean is 4.33 and RD is 7.625 • Spread: Both have the same range of 9 so they are equally wide. Planters has a stdDev of 3 and Rainbow Delight has a stdDev of 2.92. Overall both have an equal spread but Planters has a much lower amount of M&Ms per serving size than Wegman’s Brand

  10. Quantitative Data – Product vs. Cashews • Shape: Planters has a right skew but the shape of RD looks unimodal • Center: Planters mean is 1.25 and RD is 2.714 • Spread: Rainbow Delight has a higher range of 6 which means a wider spread when compared to Planters with has a range of 4. Planters has a stdDev of 1.8929 and Rainbow Delight has a stdDev of 2.058. Overall, both have little average amounts of cashews in them when compared to other pieces but of these two brands Wegman’s brand has a larger average cashews.

  11. Quantitative Data – Product vs. Raisins • Shape: Both brands look unimodal for Raisins • Center: Planters mean is 9.333 and RD is 18.5 • Spread: Rainbow Delight has a smaller range of 3 but Planters is much wider with 9. Planters has a stdDev of 3.559 and Rainbow Delight has a stdDev of 1.29. Overall, Rainbow Delight’s average is higher than Planters per serving but there only 4 samples from Rainbow delight so the data might not be justified.

  12. Quantitative Data – Product vs. Almonds • Shape: Planters is right skewed but RD looks unimodal • Center: Planters mean is 2.6667 and RD is 4.8333 • Spread: Rainbow Delight has a larger range of 9 but Planters is smaller with 5. Planters has a stdDev of 1.751 and Rainbow Delight has a stdDev of 3.430. Overall, Rainbow Delight’s average is higher than Planters per serving and RD’s mean matches Planter’s max and the Q1 for both are the same at 2.

  13. 1 Samp T Interval Conditions: • SRS • Pop>10n • Normal Popor > 30 • Random weighing • There are more than 300 servings of trail mix; there is more than 310 servings of trail mix • 30>30; 31>30 Conditions Med >> Students’ t-model >> 1 Samp T Interval

  14. 1 Sample T Interval: Rainbow Delight weight per serving • N = 31, df = 30 • Sample mean = 36.0323 • 36.0323 + 2.424 • We are 95% confident that the true mean of grams per serving of Wegmans Trail Mix from Wegmans is between 33.6075 and 38.457

  15. 1 Sample T Interval: Planters Trail Mix weight per serving • N = 30, df = 29 • Sample mean = 34.9 • 34.9 + 3.449 • We are 95% confident that the true mean of grams per serving of Planters Trail Mix from Wegmans is between 31.451 and 38.451

  16. Chi-Squared GOF Conditions • Categorical Data? • SRS? • All expected cell counts > 5? • Yes, both • Stated, both • Yes all expected for both > 5

  17. Chi-Squared GOF Test - Planters Ho: The observed frequency distribution of pieces fits the expected distribution. Ha: The observed frequency distribution of pieces does not fit the expected distribution (218-76.4)²+(60-76.4)²+…=398.49476.44 76.4 76.4 P( >398.4947|df=4)= 5.88x10-85 We reject the Ho because our p-value is < alpha which is .05. We have sufficient evidence that the observed frequency distribution of pieces does not fit the expected distribution.

  18. Chi-Squared GOF Test – Rainbow Delight Ha: The observed frequency distribution of pieces does not fit the expected distribution Ho: The observed frequency distribution of pieces fits the expected distribution. (636-217.1)²+(226.5-217.1)²+…=1131.527867 217.1 217.1 P( >1131.527867|df=4)= 0 We reject the Ho because our p-value is < alpha which is .05. We have sufficient evidence that the observed frequency distribution of pieces does not fit the expected distribution.

  19. Bias & Error • Some peanuts were still together while others were split in half • I counted both as one(1). • Raisins were sometimes conjoined • While counting one would fall on the floor • Human error of counting/Loss of Precision • I got hungry !

  20. Personal Opinions & Conclusion • Planters is tastier • More convenient than a giant tub • Based of the GOF tests, neither have uniformly distributed pieces. • The Rainbow Delight has an accurate serving size based on the confidence interval and the claim on the tub. • The serving size for Planters is higher based on the confidence interval compared to the claim on the bag.