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By: John Marron Nicole Scamuffo

JOLLY RANCHERS. By: John Marron Nicole Scamuffo. DESCRIPTION OF TOPIC. Distribution of color Time it takes to dissolve: w arm vs. cold water stirring vs. not stirring . HISTORY OF JOLLY RANCHERS . Originally produced by Jolly Rancher Company

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By: John Marron Nicole Scamuffo

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  1. JOLLY RANCHERS By: John Marron Nicole Scamuffo

  2. DESCRIPTION OF TOPIC • Distribution of color • Time it takes to dissolve: • warm vs. cold water • stirring vs. not stirring

  3. HISTORY OF JOLLY RANCHERS • Originally produced by Jolly Rancher Company • Founded in 1949 by Bill and Dorothy Harmsen • Sold to Beatrice Foods in 1966 • Purchased by Leaf Candy Company in 1983 • 1996 Hershey bought the Jolly Rancher Candy Company

  4. NEED TO KNOW • We used the “original” Jolly Rancher which contain 5 flavors: Blue RaspberryCherry Grape Green Apple Watermelon

  5. OBSERVATIONAL STUDY • 1 bag of Jolly Ranchers from 3 stores = 3 bags • Each bag is estimated to have 66 hard candies • Claimed that the colors are evenly distributed within bags • Grouped colors together from all 3 bags

  6. CHI- SQUARED GRAPH

  7. ANALYSIS & CONCLUSION • Larger overall total: • Red and blue • Smallest overall total: • Purple • Green and pink have around same count • Different stores have different amounts • Based off of this data we feel; • Jolly Rancher company doesn’t fill the bags evenly

  8. CHI-SQUARE GOODNESS OF FIT ASSUMPTIONS STATE • SRS • All expected counts ≥ 5 CHECK • assumed • All expected counts ≥ 5

  9. CHI-SQUARE GOODNESS OF FIT • Ho: the observed frequency distribution of Jolly Rancher color fits the expected distribution • Ha: the observed frequency distribution of Jolly Rancher color doesn’t fit the expected distribution P(x2> 1.0456Idf =4) = 0.903 • We fail to reject Ho because the p-value >α= 0.05 • We have sufficient evidence that the observed frequency distribution of Jolly Rancher color fits the expected distribution

  10. WARM VS. COLD 1. Determine whether candy dissolves faster in hot water or cold water • Heated up half in the microwave for 5 minutes and refrigerated other half

  11. WARM VS. COLD 2. Place 50 jolly ranchers into plastic cups that hold ¼ cup of warm water 3. Place 50 jolly ranchers into plastic cups that hold ¼ cup of cold water • Used calc for random sample

  12. WARM VS. COLD 4. Record the amount of time it takes for each jolly rancher to dissolve in the water 5. Perform a 2 sample t-test

  13. 2 SAMPLE T-TEST GRAPH

  14. ANALYSIS & CONCLUSION • As you can see in the two box plots: • Hot water: • Minimum: 22.69 –outlier • Maximum: 50.5 • Mean: 30.97 • Q1: 35.22 • Q3: 42.43 • IQR: 7.21 • Cold water: • Minimum: 61.4 –outlier • Maximum: 87.46—outlier • Mean: 75.04 • Q1: 71.91 • Q3: 76.23 • IQR: 4.32 • ** cold water seemed to have a lot of outliers • Hot water graph is left skewed • Cold water graph is symmetric • Based off of the graphs , we believe that it takes longer for a Jolly Rancher to dissolve in cold water than it take for one to dissolve in warm water

  15. 2 SAMPLE T-TEST (pooled) ASSUMPTIONS STATE • 2 independent SRS • 2 normal pops or n1 and n2 ≥ 30 • S1= S2 CHECK • Assumed • n1 and n2 ≥ 30 • N1 = 50 • N2 = 50 • 5.6 = 5.1

  16. 2 SAMPLE T-TEST POOLED Ho: µw = µc Ha: µw < µc P(t> -33.44I df = 98 ) = < 0.0001 • We reject Hobecause the p-value is < α= 0.05. • We have sufficient evidence that the mean of dissolving a Jolly Rancher in warm water is less than the mean of dissolving a Jolly Rancher in cold water

  17. STIRRING VS. NOT STIRRING 1. Heated up water for 5 minutes 2. Placed ¼ cup of water into 30 plastic cups containing 1 Jolly Rancher 3. Stirred water with a plastic knife until J.R dissolved

  18. STIRRING VS. NOT STIRRING 4. Recorded times 5. Perform 2 sample t-test to determine if stirring has an effect on the amount of time the candy took to dissolve • reused warm water data

  19. STIRRING VS. NOT STIRRING GRAPH

  20. ANALYSIS & CONCLUSION • The graphs show that: • Both graphs are left skewed • Stirring = more clustered and a more extreme skew • Based off of the data we feel that a Jolly Rancher will dissolve faster in warm water while being stirred rather than just sitting in the warm water • Hot water + stirring: • Minimum: 18.04 • Maximum: 27.59 • Mean: 23.53 • Q1: 21.66 • Q3: 25.6 • IQR: 3.94 • Hot water: • Minimum: 22.69 –outlier • Maximum: 50.5 • Mean: 30.97 • Q1: 35.22 • Q3: 42.43 • IQR: 7.21

  21. 2 SAMPLE T-TEST ASSUMPTIONS STATE • 2 independent SRS • 2 normal pops or • n1 and n2 ≥ 30 CHECK • Assumed • n1 and n2 ≥ 30 • N1 = 50 • N2 = 30

  22. 2 SAMPLE T-TEST Ho: µw = µs Ha: µw > µs P(t> -16.57I df = 73.469 ) = < 0.0001 • We reject Hobecause the p- value is < α= 0.05. • We have sufficient evidence that the mean of dissolving a Jolly Rancher in warm water without stirring is greater than the mean of dissolving a Jolly Rancher in warm water while stirring = -16.57

  23. APPLICATION • Applies to people who purchase Jolly Ranchers • Getting a good deal—colors seem to be equally distributed • Melt faster in a warm environment (mouth)

  24. BIAS/ERROR • 1st study– only took bags from Buck County area • Most likely same distribution center • 2nd test– water temperature changed as it sat • Both ended up at room temp • 3rd test– different stirring techniques

  25. PERSONAL OPINIONS • Too much work to do in too little time • Not every store had Jolly Ranchers • Jolly Ranchers took too long to dissolve • Cold water took over an hour • Surprised at the time difference between the temperature waters

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