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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
en
au
rdis
2
4
6
8
10
G
Marshmallow_Count
0 5 10 15 20 25 30 35
Genaurdis Histogram
Gen
au
rdis
-2
-1
0
1
2
G
Marshmallow_Count
0 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: Genaurdis
Genaurdis
Marshmallow_Count
17.3
8
14.5
17
20.5
28
4.86326
S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = s
G
Marshmallow_Count
0 5 10 15 20 25 30
Genaurdis Box Plot
Marshmallow Count: AcmeA
cm
e
-2
-1
0
1
2
A
Marshmallow_Count
0 5 10 15 20 25 30
Normal Quantile (A) = 0.206Marshmallow _Count - 3.14
Acme Normal Quantile Plot
Acm
e
1
2
3
4
5
6
A
Marshmallow_Count
0 5 10 15 20 25 30
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
Marshmallow_Count
0 5 10 15 20 25 30
Acme Box PlotAcme
Marshmallow_Count
15.225
8
12
15
19
27
4.84365
S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = s
Marshmallow Count: WegmansW
eg
man
s
-2
-1
0
1
2
W
Marshmallow_Count
0 5 10 15 20 25 30
Normal Quantile (W) = 0.201Marshmallow _Count - 3.17
Wegmans Normal Quantile Plot
Weg
man
s
2
4
6
8
10
12
W
Marshmallow_Count
0 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
Wegmans
Marshmallow_Count
15.8
6
12.5
16
19
29
4.98305
S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = s
W
Marshmallow_Count
0 5 10 15 20 25 30
Wegmans Box Plot
Marshmallow Count: All Together
05
1015
202530
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
ST
OR
E
0
4
8
12
A
0
4
8
12
G
4
8
12
W
Marshmallow_Count
0 5 10 15 20 25 30 35
All Together Histogram
AG
W
Marshmallow_Count
0 5 10 15 20 25 30
All Together Box Plot
All Together
Marshmallow_Count
16.1083
6
12
16
19
29
4.93452
S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = s
Survey: Age Group & Age Group with Preference
5
10
15
20
25
30
35
40
Age_Group
A E K T
count
Survey Bar Chart
Wit
h_o
r_W
ith
ou
t_M
arsh
mal
low
s
0
10
20
30
N
10
20
30
Y
Age_Group
A 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
Gender
F M
count
Survey Bar Chart
Wit
h_o
r_W
ith
ou
t_M
ars
hm
allo
ws
0
20
40
60
N
20
40
60
Y
Gender
F 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
• 15.225 + 1.54907• We are 95% confident that the true
mean of marshmallows per packet from Acme is between 13.6759 and 16.7741 marshmallows.
1SampTInterval: Wegmans Marshmallows per packet
• 15.8 + 1.59366• We are 95% confident that the true
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