Sour Patch final

Report
How sweet of a deal are you
really getting?
By Kelly Culp, Ashley Hall, and Amanda Simo
 We
wanted to research how many Sour
Patch Kids were distributed in a bulk
bag
 From there we wanted to see if the
weight of the actual candies was equal
to the claim on the package
 To do this we purchased bulk bags from
both Costco and BJs

We calculated the number, color, and
weight of the Sour Patch Kids in each
mini packet
A BRIEF HISTORY ON THE LIFE OF SOUR
PATCH KIDS
Sour Patch Kids started as Mars Men – which
were sold as one cent a piece
 The inspiration occurred during a time when
UFO sighting were exciting



Idea of a sour-coated soft candy with an “out of this
world” tartness was developed in the late 1970s
Believed that Frank Galatolie came up with idea
of introducing sour products in soft confectionery
category and experiment with cherry candy
products

New product was named Sour Patch Kids and
distributed in the US in 1985
PROCEDURE
In order to collect our data, we purchased bulk
bags from Costco and BJs
 We took out the Swedish fish packets, and
counted the Sour Patch Kids packets
 For each packet, we calculated the weight with a
scale (in grams)
 We counted each color for the population of each
bag, and the population of

DISTRIBUTION OF COLORS
Collection 1
Green
Red
25%
24%
Orange
Yellow
25%
26%
Green
S1 =
S2 =
S3 =
S4 =
S5 =
S6 =
Red
Orange
Yellow
1.67857
1.63571
1.77143
1.64286
0
0
0
0
1
1
1
1
2
2
2
1.5
2
2
3
2
5
6
5
7
mean
min
Q1
median
Q3
max
Distribution of the population of sour patch colors remains
very even. The means all colors fall within the 1.6-1.7 range.
FREQUENCY HISTOGRAMS FOR COLORS
Range:
0-5
Range:
0-5
Range:
0-7
Range:
0-6
Distributions are slightly right skewed and unimodal.
Red and yellow colored sour patch have outliers.
Yellow has
a outlier of
7 and red
has an
outlier of 6.
HISTOGRAM AND SCATTER PLOTS
Our histograms show that the
sour patch kids packets have a left
skewed distribution, and are
unimodal. Our range for the
amount in each packet is from 010.
Our scatter plot shows that the
weight and amount of sour
patch kids is linear. As the
amount of sour patch kids in
each packet increases, the
weight of the packet increases.
BOX PLOTS
* These box plots appear similar because
as we showed before, the amount and
weight have a linear relationship.
Our box plot shows that BJs appears
to have a more even distribution of the
amount of candies, and only two
outliers. While Costco has 6 outliers.
Costco has a greater range and smaller
IQR, while BJs has a much large IQR
but a smaller range.
The weight of the candies
appears to be slightly left
skewed for both box plots
between both stores. However,
Costco has a smaller IQR, while
BJs has a smaller range.
CONCLUSIONS ABOUT OUR POPULATION
Colors of the candies are evenly distributed
 The population of each color in each packet range
from 0-7
 Both yellow and red had outliers
 The distribution of the amount of candies is left
skewed, and unimodal



Mode = 8
Costco appears to have a lot more outliers and
smaller IQR, but a greater range than BJs

Costco’s distribution is more random
ASSUMPTIONS FOR 1 SAMPLE T-TEST
(TO SEE IF THE 15.0 CLAIM FITS)
STATE
1)
2)
3)
SRS
Pop ≥ 10n
Normal population
or n ≥ 30
CHECK
1.
2.
3.
Assumed
representative
Population of all
Sour Patch Kids
packets is greater
than 1,400
140 ≥ 30
Conditions met → Student’s t-distribution → 1 sample t-test
1 SAMPLE T-TEST MECHANICS
H 0 :   15
Collection 1
Weight
13.0724 g
3.6176 g
S1 = mean
S2 = s
H A :   15
x 
13.0724 – 15
t
- 6.3041
=
=
3
.
6176
/
140
s
n
2 * P(t< -6.3041│df =139) = 3.5860 * 10-9



We reject the H0 because the p value of 3.5860 * 10-9 is less
than alpha = .05.
We have sufficient evidence that the true mean of the
weight of sour patch kids per bag is not equal to15 grams.
The stated weight on the outside of the bag incorrectly
estimates the actual weight of the sour patch kids.
CHI-SQUARE GOODNESS OF FIT TEST FOR
COLOR
STATE
1)
2)
3)
CHECK
Categorical Data
SRS
All expected counts ≥
5
1)
2)
3)
Yellow
Colors are
categorical
Assumed
representative
All expected counts
are greater than 5
Green
Red
Orange
Observed 230
235
229
248
Expected
235.5
235.5
235.5
235.5
Conditions met →
 2 distribution →  2 GOF test
MECHANICS
(observed  expected) 2 (230 235.5) 2 (235 235.5) 2
x 


 ...  .9724
(expected)
235.5
235.5
2
p(x²›.9724│df=3)= .8079
We fail to reject the Ho because our p-value
of .8079 is greater than = .05.
We have sufficient evidence that the color
Sour Patch Kids in the tiny packets are evenly
distributed.
1 SAMPLE T-INTERVAL (95% CONFIDENCE)
STATE
1)
2)
3)
SRS
Population ≥ 10n
Normal population
or n ≥ 30
CHECK
1)
2)
3)
Assumed
representative
All Sour Patch Kids
packets are greater
than 1,400
Normal population
displayed on graph
Conditions met → Student’s t-distribution → 1 sample t-interval
1 SAMPLE T-INTERVAL MECHANICS
x t
*
s
3.6176
= 13.0724 1.9772
=
n
140
(12.468,13.677)
We are 95% confident that the true mean of
the weight of the bags of sour patch kids is
between 12.468 and 13.677 grams.
CHI-SQUARE HOMOGENEITY FOR COLOR VS.
STORE
STATE
1)
2)
3)
CHECK
Categorical Data
SRS
All expected counts ≥
5
1)
2)
3)
Conditions met →
Colors are
categorical
Assumed
representative
All expected counts
are greater than or
equal to 5
 2 distribution → Test for Homogeneity
HYPOTHESIS
Ho: The distribution of colors within the sour
patch kids bags has no association to the store
they were bought at.
 Ha: The distribution of colors within the sour
patch kids bags has an association to the store
they were bought at.

df = 3
MECHANICS
Yellow
Green
Red
Orange
BJs
108 (113.9)
127 (116.37)
109 (112.91)
121 (121.82)
Cosco
122 (116.1)
108 (118.63)
119 (115.09)
125 124.18)
(observed  expected) 2 (108 113.9) 2 (127 116.37) 2
x 


 ...  2.806
(expected)
113.9
116.37
2
p(x²›2.806│df=3)= .4225
We fail to reject the Ho because our p-value
of .4225 is greater than = .05.
We have sufficient evidence that the
distribution of colors within the sour patch
kids bags has no association to the store they
were bought at.
PERSONAL OPINIONS/ CONCLUSIONS


The data was really hard to collect
 Tedious and Long
 Some were not full Sour Patch Kids so we had to use our
judgment
They are really good
 Had no problem eating them
 A mountain of Sour Patch Kids

Should have purchased from a wide range of stores

Hard to tell the true distribution, as some packaging of Sour
Patch kids are sold differently
Interesting experiment
 The distributions are fairly accurate
 The weight of the packets are below the stated weights

APPLICATION
When buying the packets of Sour Patch Kids, in
the bulk size bags, you have a good chance of
getting an even amount of each color
 HOWEVER, this is only if you go through each
packet


Some packets had 0 Sour Patch, and some had only
one color!
When buying Bulk Bags from Cosco, you are
more likely to get outliers, meaning you have a
greater chance of getting some with a lot of
candies or very few
 Either way, the amount does not equal the 15
gram claim!

BIAS / ERROR

Human error
When quickly counting the colors and weight we may
have forgotten to zero the scale
 The weight of the sugar may have added, some bags
had lots more sugar than others

Only counted data from two stores: Cosco and
BJs
 These are only one type of packaging, Sour Patch
Candies come in all sorts of ways to buy


These may have different distributions
CONCLUSION
The amount of Sour Patch Kids in each bag does
not equal 15 grams, the expected interval is
between 12.468 and 13.677 grams
 There is an even distribution between colors,
when looking at the amount in all the packets
 The amount of candies in each packet is not
evenly distributed


Distribution is left skewed

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