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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

JOLLY RANCHERS

By: John Marron

Nicole Scamuffo

slide2

DESCRIPTION OF TOPIC

  • Distribution of color
  • Time it takes to dissolve:
    • warm vs. cold water
    • stirring vs. not stirring
slide3

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
slide4

NEED TO KNOW

  • We used the “original” Jolly Rancher which contain 5 flavors:

Blue RaspberryCherry

Grape

Green Apple

Watermelon

slide5

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
slide7

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
slide8

CHI-SQUARE GOODNESS OF FIT

ASSUMPTIONS

STATE

  • SRS
  • All expected counts ≥ 5

CHECK

  • assumed
  • All expected counts ≥ 5
chi square goodness of fit
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
slide10

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
slide11

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
slide12

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

slide14

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
slide15

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
slide16

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
slide17

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

slide18

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
slide20

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
slide21

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
slide22

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

slide23

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)
slide24

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
slide25

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