By: Rochelle Cooper,
Jon Hale, and Ainsley
Hume
• It was created in 1963 by the Vice President of the
General Mills Company, John Holahan
• It was created, at first, by taking orange marshmallow
peanuts, cutting them up, and sprinkling them over
cheerios
• Pink hearts, yellow moons, orange stars, and green
clovers were the first in the box. Next came blue
diamonds, purple horseshoes, followed by red balloons.
After came rainbows, pots of gold and Leprechaun hats
• All these combined to make the delicious cereal
Reason for picking topic
• We decided that we wanted to measure
the proportion of items in a type of food
• Had to be able to measure it accurately
(not extremely hard)
• All like Lucky Charms cereal
Boxplot for initial weight of
Lucky Charms Mini Boxes
•Weight in grams
•Weight on box= 48.19g
•Min.=61.28g
•Q1=62.9g
•Median=63.89g
•Q3=65.89g
62.9g
61.28g
65.89
71.73g
63.89g
60 62 64 66 68 70
•Max=71.73g
•IQR=Q3-Q1=(65.89g)-(62.9g)=2.99g
72 74
Outliers for initial weight of
Lucky Charms Mini Boxes
•IQR=Q3-Q1=(65.89g)-(62.9g)=2.99g
•Outlier test
Q3+[IQR(1.5)]=High limit:70.375g
Q1-[IQR(1.5)]=High limit:70.375g
1 outlier: #25, 71.73g
62.9g
61.28g
65.89
68.04g
71.73g
63.89g
60 62 64 66 68 70
72 74
Boxplot for proportion of
marshmallows in Lucky Charms
•Min.=.1456
Mini Boxes
•Q1=.1898
.146
•Median=.2421
19
.276
.242
•Q3=.2464
•Max=.3777
.1
.2
•IQR=Q3-Q1=(.2464)-(.1898)=.0566
•Outlier test
Q3+[IQR(1.5)]=High limit:1.0954
Q1-[IQR(1.5)]=High limit:-.6592
No outliers
.377
.3
.4
Histogram for proportion of
marshmallows in Lucky Charms
Mini Boxes
•X-axis:proportion of marshmallows
•Y-axis:frequency
•Right skewed
•
x
=.24
11
•Range=.24
0
.14 .16 .18 .2 .22 .24 .26 .28 .3 .32 .34 .36 .38
-6
Proportion of Marshmallows
Scatterplot for proportion of
marshmallows in Lucky Charms
Mini Boxes
•Slightly
positive
direction
•Moderately
weak
•Linear
25
20
15
10
5
40 45 50 55
60
65
Mini Boxes total Weight in grams
Assumptions for 1-Proportion
Z-Test
1.SRS
2.np 10
n(1-p) 10
3.pop 10  n
1.assumed
2.1749(.272)  10
1749(.728)  10
3.pop 10(1749)
1-Proportion Z-Test
Ho: p=.272
Ha: p .272
Z=
pˆ  p = -1.9198
p (1  p )
n
2*P(z<-1.9198)=.054879
We fail to reject the Ho because p>.05= . We have
sufficient evidence that the proportion of marshmallows
is equal to .272.
Assumptions for T-Test of
Marshmallow Weight
1.SRS
2.Normal population
or
n 30
1.assumed
2.34 30
T-Test of Marshmallow Weight
Ho :   13.1087
Ha :   13.1087
x  12.6562
n  34
x
t
 1.1675
s n
2  P (t  1.1675)  .25137
We fail to reject the Ho because p>.05= . We have
sufficient evidence that the mean marshmallow weight is
equal to 13.1087 grams.
Assumptions for T-Test of
Serving Size Weights
1.SRS
1.assumed
2.Normal population
2.34 30
or
n 30
T-Test of Serving Size Weights
Ho :   49
Ha :   49
x
t
 8.041984
s n
2  P (t  8.041984)  2.7987  10^ 27
We reject the Ho because p<.05=  . We have sufficient
evidence that the mean serving size weight is not equal to
49 grams.
Confidence Interval
x  t * ( s  n )  (51.251,52.775)
We are 95% confident that the mean serving size
weight is between 51.251 and 52.775 grams.
Bias
• Packaging bias
• Lack of mini-cereals in grocery stores
– Not many, plus only stocked in
Genardi’s
• Bias during weighing
– Scale might not be exact
– Losing pieces of cereal
• Calculating population proportion
– Had to round up for 1-proportion ztest
• Bag added extra weight
Conclusions
• The marshmallows were close enough to the
mean weight, 13.1087 grams.
• The cereal was not always the right weight
– Generally over the mean weight…good for
us!
• The proportion of marshmallows to cereal
was close enough to the mean proportion,
.272.
– However, at .01 alpha level, we would
reject the Ho.
Our Conclusions
• The mean serving size weights seemed to be
very spread out. This was surprising as I would
expect the company to keep it close to or
under the mean weight of 49 grams
• Visually, thought the weights would be
different because the marshmallows in the
containers looked not as appetizing as the
marshmallows in the box
• Surprised at how high the outlier was
compared to the mean weight of 49 grams