### Jolly Ranchers

```By: John Marron
Nicole Scamuffo
• Distribution of color
• Time it takes to
dissolve:
–warm vs. cold water
–stirring vs. not
stirring
• 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
• We used the “original” Jolly Rancher
which contain 5 flavors:
Blue Raspberry
Cherry
Grape
Green Apple
Watermelon
• 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
50
45
40
35
30
Genuardi's
25
Wegmans
Target
20
15
10
5
0
Color Distribution
Purple
Red
Green
Pink
Blue
• 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
STATE
• SRS
• All expected counts
≥5
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
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
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
4. Record the amount
of time it takes for
each jolly rancher to
dissolve in the water
5. Perform a 2 sample ttest
Box Plot
Jolly Rancher
Jolly Rancher
hot_w ate r_not_s tirring
38.969
22.67
35.22
40.69
42.43
50.5
7.21
20
25
30
35
40
45
hot_w ater_not_stirring
50
55
S1
S2
S3
S4
S5
S6
S7
=
=
=
=
=
=
=
mean
min
Q1
median
Q3
max
iqr
Jolly Rancher
Box Plot
Jolly Rancher
cold_w ate r_not_s tirring
75.0384
61.4
71.91
74.29
76.23
87.46
4.32
60
65
70
75
80
cold_w ater_not_stirring
85
90
S1
S2
S3
S4
S5
S6
S7
=
=
=
=
=
=
=
mean
min
Q1
median
Q3
max
iqr
• 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
•Hot water graph is left skewed
have a lot of outliers
•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
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
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
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
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
Jolly Rancher
Box Plot
Jolly Rancher
Stirring_in_w arm _w ater
23.5303
18.04
21.66
23.975
25.6
27.59
3.94
18
20
22
24
Stirring_in_w arm _w ater
26
28
Box Plot
Jolly Rancher
S1
S2
S3
S4
S5
S6
S7
=
=
=
=
=
=
=
mean
min
Q1
median
Q3
max
iqr
Jolly Rancher
hot_w ate r_not_s tirring
38.969
22.67
35.22
40.69
42.43
50.5
7.21
20
25
30
35
40
45
hot_w ater_not_stirring
50
55
S1
S2
S3
S4
S5
S6
S7
=
=
=
=
=
=
=
mean
min
Q1
median
Q3
max
iqr
• The graphs show that:
Hot water:
Minimum: 22.69 –outlier
Maximum: 50.5
Mean: 30.97
Q1: 35.22
Q3: 42.43
IQR: 7.21
Hot water + stirring:
Minimum: 18.04
Maximum: 27.59
Mean: 23.53
Q1: 21.66
Q3: 25.6
IQR: 3.94
• 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
STATE
• 2 independent SRS
CHECK
• Assumed
• 2 normal pops
or
• n1 and n2 ≥ 30
• n1 and n2 ≥ 30
• N1 = 50
• N2 = 30
Ho: µw = µs
Ha: µw > µs
= -16.57
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
• Applies to people who purchase Jolly Ranchers
– Getting a good deal—colors seem to be equally
distributed
• Melt faster in a warm environment (mouth)
• 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
• 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
```