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