Sour Patch Kids
How sweet of a deal are you really getting?
By Kelly Culp, Ashley Hall, and Amanda Simo
OVERVIEW OF OUR PROJECTWe 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 BJsWe 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
24%
26%24%
25%
Red
Orange
Yellow
Green
Collection 1
Green Red Orange Yellow
1.67857
0
1
2
2
5
1.63571
0
1
2
2
6
1.77143
0
1
2
3
5
1.64286
0
1
1.5
2
7
S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = 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
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.
Range: 0-5 Range:
0-7
Range: 0-5
Range: 0-6
0
2
46
8
1012
14
1618
20
22
Amount
0 2 4 6 8 10 12
Collection 1 Scatter Plot
HISTOGRAM AND SCATTER PLOTS
10
20
30
40
50
-2 0 2 4 6 8 10 12
Amount
Collection 1 Histogram 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 0-10.
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 PLOTSB
JsC
osco
Amount
0 2 4 6 8 10 12
Collection 1 Box Plot
BJs
Cos
co
Weight (grams)
0 2 4 6 8 10 12 14 16 18 20 22
Collection 1 Box Plot
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.
* These box plots appear similar because as we showed before, the amount and weight have a linear relationship.
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)
1) SRS2) Pop ≥ 10n3) Normal population
or n ≥ 30
1. Assumed representative
2. Population of all Sour Patch Kids packets is greater than 1,400
3. 140 ≥ 30
STATE CHECK
Conditions met → Student’s t-distribution → 1 sample t-test
1 SAMPLE T-TEST MECHANICS Collection 1
Weight g13.0724
g3.6176
S1 = meanS2 = s
xt
s
n
13.0724 – 15
=
140/6176.3 =
- 6.3041
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.
15:
15:0
AH
H
CHI-SQUARE GOODNESS OF FIT TEST FOR COLOR
1) Categorical Data2) SRS3) All expected counts
≥ 5
1) Colors are categorical
2) Assumed representative
3) All expected counts are greater than 5
STATE CHECK
Yellow Green Red Orange
Observed
230 235 229 248
Expected
235.5 235.5 235.5 235.5
Conditions met → distribution → GOF test 2 2
MECHANICS
9724....5.235
)5.235235(
5.235
)5.235230(
)(exp
)exp( 2222
ected
ectedobservedx
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)
1) SRS2) Population ≥ 10n3) Normal population
or n ≥ 30
1) Assumed representative
2) All Sour Patch Kids packets are greater than 1,400
3) Normal population displayed on graph
STATE CHECK
Conditions met → Student’s t-distribution → 1 sample t-interval
1 SAMPLE T-INTERVAL MECHANICS
* sx tn
=140
6176.39772.10724.13 =
(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
1) Categorical Data2) SRS3) All expected counts
≥ 5
1) Colors are categorical
2) Assumed representative
3) All expected counts are greater than or equal to 5
STATE CHECK
Conditions met → distribution → Test for Homogeneity
2
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.
MECHANICSYellow 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)
806.2...37.116
)37.116127(
9.113
)9.113108(
)(exp
)exp( 2222
ected
ectedobservedx
df = 3
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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