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Trail Mix Statistics

Trail Mix Statistics. By Tyler Lipshutz. 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).

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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.

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