the adventures of the swiss miss marshmallows

The Adventures of the Swiss Miss Marshmallows

By Skyler Northcutt &Vivian Skumpija

Description of Project• We planned to research how many

marshmallows are packaged in one packet of Swiss Miss Hot Chocolate with marshmallows.– See how the amount of marshmallows was

distributed per packet• We surveyed a total of 100 people at Wegmans

to find out their preference in relation to drinking hot chocolate with or without marshmallows– Charted their gender, age group, and preference– Did this in order to randomize our voluntary response

sample

Swiss Miss Hot Chocolate• Sold by an American Food Company,

ConAgra Foods Inc.• Available In:

– regular and "no sugar added“– with or without small marshmallows– Great Start Cocoa (fortified with 15 essential

vitamins and minerals)– Pick-Me-Up (with 67 mg of caffeine/packet)

• For over 20 years, Swiss Miss sales remained at about 40% of national cocoa mix sales for many years

Procedure

1. At Wegmans, over a total of 4 hours, we approached every fifth person to come out of the store.

a. Made sure to survey people at various times of the day

b. Wanted to get voluntary responses from people

2. After the survey, we went on to test our numerical data

Procedure (cont.)a. Bought 4 boxes of Swiss Miss

Hot Chocolate with Marshmallows from 3 different grocery stores (Genaurdis, Acme, Wegmans)

b. Each box had 10 packets, resulting in 40 samples from each store, increasing our sample size

c. In their store grouping, we opened the packets and sifted through the hot chocolate in order to count all the marshmallows in one packet.

d. We repeated this process for each of the 40 packets from the different stores.

Marshmallow Count: GenaurdisG

enau

rdis

2

4

6

8

10

G

Marshmallow _Count0 5 10 15 20 25 30 35

Genaurdis Histogram

Gen

aurd

is

-2

-1

0

1

2

G

Marshmallow _Count0 5 10 15 20 25 30

Normal Quantile (G) = 0.206Marshmallow _Count - 3.56

Genaurdis Normal Quantile Plot

•Histogram: Unimodal, roughly symmetric, (8,28), center roughly at 17•Normal Quartile Plot: Strong and Linear= normal model

• Only whole numbers

Marshmallow Count: GenaurdisGenaurdis

Marshmallow_Count

17.38

14.517

20.528

4.86326S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = s

G

Marshmallow_Count0 5 10 15 20 25 30

Genaurdis Box Plot

Marshmallow Count: AcmeA

cme

-2

-1

0

1

2

A


Normal Quantile (A) = 0.206Marshmallow _Count - 3.14

Acme Normal Quantile Plot

Acm

e

1

2

3

4

5

6

A


Acme Histogram

•Histogram: One mode with numerous peaks, slightly right skewed, (8,27), center roughly at 15, gap•Normal Quartile Plot: Strong and Linear= normal model

• Only whole numbers

Marshmallow Count: AcmeA


Acme Box PlotAcme

Marshmallow_Count

15.2258

12151927


Marshmallow Count: WegmansW

egm

ans

-2

-1

0

1

2

W


Normal Quantile (W) = 0.201Marshmallow _Count - 3.17

Wegmans Normal Quantile Plot

Weg

man

s

2

4

6

8

10

12

W

Marshmallow_Count0 5 10 15 20 25 30 35

Wegmans Histogram

•Histogram: Unimodal, roughly left skewed, (6,29), center roughly at 16, outlier at 29•Normal Quartile Plot: Strong and Linear= normal model

• Outlier• Only whole numbers

Marshmallow Count: Wegmans

WegmansMarshmallow _Count

15.86

12.5161929


W


Wegmans Box Plot

Marshmallow Count: All Together

05

1015202530

Normal QuantileSTORE

-2 -1 0 1 2A

-2 -1 0 1 2G

-2 -1 0 1 2W

Marshmallow _Count = 4.84(Normal Quantile (A)) + 15

Marshmallow _Count = 4.86(Normal Quantile (G)) + 17

Marshmallow _Count = 4.98(Normal Quantile (W)) + 16

All Together Normal Quantile Plot

STO

RE

048

12

A

048

12

G

48

12

W

Marshmallow_Count0 5 10 15 20 25 30 35

All Together Histogram

AG

W


All Together Box Plot

All TogetherMarshmallow _Count

16.10836

12161929


Survey: Age Group & Age Group with Preference

5

10

15

20

25

30

35

40

Age_GroupA E K T

count

Survey Bar Chart

With

_or_

With

out_

Mar

shm

allo

ws

0

10

20

30

N

10

20

30

Y

Age_GroupA E K T

count

Survey Bar Chart

•Key: A- Adult, E- Elderly, K-Kid, T-Teen•Majority of adults and elderly surveyed •Most people prefer marshmallows in their hot chocolate

Survey: Gender & Gender with Preference

10

20

30

40

50

60

70

GenderF M

count

Survey Bar Chart

With

_or_

With

out_

Mar

shm

allo

ws

0

20

40

60

N

20

40

60

Y

GenderF M

count

Survey Bar Chart

•Key: F-Female M-Male•Majority of females surveyed•Most people prefer marshmallows in their hot chocolate

T-Intervals Of Marshmallow Count Conditions

1.SRS2.Pop >10n3.Normal

population or > 30

1.Randomized sampling

2.There are more than 400 packets of Swiss Miss Hot Chocolate; there are more than 1200 packets also

3.40 > 30, 120 >30

All conditions met, Students’ t model, 1sampTintervalDf= 39, Df= 119

1SampTInterval: Genaurdis Marshmallows per packet

• 17.3 + 1.55535• We are 95% confident that the true

mean of marshmallows per packet from Genaurdis is between 15.7447 and 18.8553 marshmallows.

1SampTInterval: Acme Marshmallows per packet


mean of marshmallows per packet from Acme is between 13.6759 and 16.7741 marshmallows.

1SampTInterval: Wegmans Marshmallows per packet


mean of marshmallows per packet from Wegmans is between 14.2063 and 17.3937 marshmallows.

1SampTInterval: All Together Marshmallows per packet

• 16.1083 + .891952• We are 95% confident that the true

mean of marshmallows per packet from all three stores combined is between 15.2164 and 17.0003 marshmallows.

Chi-Square Test for Gender and Marshmallow Preference

• Goodness of Fit• DF= 1• Conditions

1.Categorical Data

2.SRS3.All expected

counts > 5

1. Gender and Preference are categorical

2. Random 100 people survey sample

3. All expected counts > 5

First attribute: Gender Number of categories: 2Second attribute: With_or_Without_Marshmallows Number of categories: 2 Alternative hypothesis: There is an association betw een Gender and With_or_Without_Marshmallows

The test statistic, chi-square, is 1.082. There are 1 degrees of freedom (the number of row s minus one times the number of columns minus one).

If it w ere true that Gender w ere independent of With_or_Without_Marshmallows (the null hypothesis), and the sampling process w ere performed repeatedly, the probability of getting a value for chi-square this great or greater w ould be 0.3.

The numbers in parentheses in the table are expected counts.

RowSummary

Column Summary

Gender

M

Gender

F

N

YWith_or_Without_Marshmallows

10 (12.0) 9 (7.0)

53 (51.0) 28 (30.0)

63 37

19

81

100

Chi-Square Test for Gender and Marshmallow Preference

• Ho: there is not an association between gender and marshmallow preference

• Ha: there is an association between gender and marshmallow preference

(10-12)²+ (9-7)²+…= 1.082

12 7

P( >1.082|DF=1) = .2982

We fail to reject the Ho because the p-value .2982 > alpha =.05. We have sufficient evidence that there is no association between gender and marshmallow preference.

Chi-Square Test for Age Group and Marshmallow Preference

• Goodness of Fit• DF= 3• Conditions

1.Categorical Data

2.SRS3.All expected

counts > 5

1. Age group and Preference are categorical

2. Random 100 people survey sample

3. All expected counts > 5 (except 2)

RowSummary

Column Summary

Age_GroupAge_GroupAge_Group

E K T

Age_Group

A

N

YWith_or_Without_Marshmallows

7 (6.8) 8 (6.7) 1 (1.7) 3 (3.8)

29 (29.2) 27 (28.4) 8 (7.3) 17 (16.2)

36 35 9 20

19

81

100

Chi-Square Test for Age Group and Marshmallow Preference

• Ho: there is not an association between age group and marshmallow preference

• Ha: there is an association between age group and marshmallow preference

(7- 6.8)²+ (8- 6.7)²+…= .9148

6.8 6.7

P( >.9148|DF=3) = .8219

We fail to reject the Ho because the p-value .8219 > alpha =.05. We have sufficient evidence that there is no association between age group and marshmallow preference.

Concluding…• Through the intervals, we found

that all together, the average mean of marshmallows per packet from Swiss Miss is between15.2164 and 17.0003 marshmallows.

• Our Chi-Square tests revealed that both gender and age group have no association to drinking hot chocolate with or without marshmallows.

Application to Population• Majority of Bucks County residents

prefer marshmallows in their Hot Chocolate – Their age and gender remains

independent from this preference.• Swiss Miss Hot Chocolate sold in

Genaurdis, Acme, and Wegmans in Bucks County all appeared to have randomized marshmallow quantities per packet, having similar intervals.

Bias and Error• A person missed at Wegmans during the survey• People who chose not to answer, voluntary

response• Wrong estimation of age group• Difference in counting certain marshmallows

– Broken pieces or conjoined• Could have…

– Increased sample size– Avoided voluntary response bias some how– Gone to different places besides Wegmans

Personal Opinions• Skyler : It was

awkward approaching some of the people at Wegmans because they didn’t take me seriously. Sifting was a blast!

• Vivian : Unique process with a sifter and massive amounts of hot chocolate powder up my nostrils, my mom zip lock bagged them to save them for later consumption

the adventures of the swiss miss marshmallows

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