By: John MarronNicole Scamuffo

JOLLY RANCHERS

• Distribution of color • Time it takes to

dissolve:–warm vs. cold water–stirring vs. not

stirring

DESCRIPTION OF TOPIC

• 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

HISTORY OF JOLLY RANCHERS

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

NEED TO KNOW

Blue RaspberryCherryGrapeGreen AppleWatermelon

• 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

OBSERVATIONAL STUDY

CHI- SQUARED GRAPH

Color Distribution Purple Red Green Pink Blue0

5

10

15

20

25

30

35

40

45

50

Genuardi'sWegmans Target

• 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

ANALYSIS & CONCLUSION

STATE• SRS• All expected counts

≥ 5

CHI-SQUARE GOODNESS OF FITASSUMPTIONS

CHECK• assumed• All expected counts

≥ 5

• 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> 1.0456 Idf =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

CHI-SQUARE GOODNESS OF FIT

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

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

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

WARM VS. COLD

2 SAMPLE T-TEST GRAPH

20 25 30 35 40 45 50 55

hot_water_not_stirring

Jolly Rancher Box Plot

60 65 70 75 80 85 90

cold_water_not_stirring

Jolly Rancher Box Plot

Jolly Rancher

hot_water_not_stirring

38.969

22.67

35.22

40.69

42.43

50.5

7.21

S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = iqr

Jolly Rancher

cold_water_not_stirring

75.0384

61.4

71.91

74.29

76.23

87.46

4.32

S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = iqr

• As you can see in the two box plots:

ANALYSIS & CONCLUSION

Hot water:Minimum: 22.69 –outlier Maximum: 50.5Mean: 30.97Q1: 35.22Q3: 42.43IQR: 7.21

•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

Cold water:Minimum: 61.4 –outlier Maximum: 87.46—outlier Mean: 75.04Q1: 71.91Q3: 76.23IQR: 4.32

** cold water seemed to have a lot of outliers

STATE • 2 independent SRS• 2 normal pops or

n1 and n2 ≥ 30

• S1= S2

2 SAMPLE T-TEST (pooled)ASSUMPTIONS

CHECK• Assumed • n1 and n2 ≥ 30

N1 = 50

N2 = 50 • 5.6 = 5.1

Ho: µw = µc

Ha: µw < µc

P(t> -33.44 I df = 98 ) = < 0.0001 • We reject Ho because 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

2 SAMPLE T-TEST POOLED

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

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

STIRRING VS. NOT STIRRING

STIRRING VS. NOT STIRRING GRAPH

18 20 22 24 26 28

Stirring_in_warm_water

Jolly Rancher Box Plot

20 25 30 35 40 45 50 55

hot_water_not_stirring

Jolly Rancher Box Plot

Jolly Rancher

Stirring_in_warm_water

23.5303

18.04

21.66

23.975

25.6

27.59

3.94

S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = iqr

Jolly Rancher

hot_water_not_stirring

38.969

22.67

35.22

40.69

42.43

50.5

7.21

S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = iqr

• 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

ANALYSIS & CONCLUSION

Hot water:Minimum: 22.69 –outlier Maximum: 50.5Mean: 30.97Q1: 35.22Q3: 42.43IQR: 7.21

Hot water + stirring:Minimum: 18.04 Maximum: 27.59Mean: 23.53Q1: 21.66Q3: 25.6IQR: 3.94

STATE • 2 independent SRS

• 2 normal pops or • n1 and n2 ≥ 30

2 SAMPLE T-TESTASSUMPTIONS

CHECK• Assumed

• n1 and n2 ≥ 30

• N1 = 50

• N2 = 30

Ho: µw = µs

Ha: µw > µs

P(t> -16.57 I df = 73.469 ) = < 0.0001• We reject Ho because 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

2 SAMPLE T-TEST

= -16.57

• Applies to people who purchase Jolly Ranchers– Getting a good deal—colors seem to be equally

distributed • Melt faster in a warm environment (mouth)

APPLICATION

• 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

BIAS/ERROR

• 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

PERSONAL OPINIONS