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

•Max=71.73g

•IQR=Q3-Q1=(65.89g)-(62.9g)=2.99g

60 62 64 66 68 70 72 74

61.28g 71.73g62.9g 65.89

63.89g

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

60 62 64 66 68 70 72 74

61.28g 68.04g 71.73g62.9g 65.89

63.89g

•Min.=.1456

•Q1=.1898

•Median=.2421

•Q3=.2464

•Max=.3777

•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

Boxplot for proportion of marshmallows in Lucky

Charms Mini Boxes

.1 .2 .3 .4

.146 .377 19 .276

.242

Histogram for proportion of marshmallows in Lucky

Charms Mini Boxes •X-axis:proportion of marshmallows

•Y-axis:frequency

•Right skewed

• =.24

•Range=.24

x11

-6

.14 .16 .18 .2 .22 .24 .26 .28 .3 .32 .34 .36 .380

Proportion of Marshmallows

5

10

15

20

25

40 45 50 55 60 65Mini Boxes total Weight in grams

Scatterplot for proportion of marshmallows in Lucky

Charms Mini Boxes •Slightly positive direction

•Moderately weak

•Linear

Assumptions for 1-Proportion Z-Test

1.SRS 1.assumed

2.np 10 2.1749(.272) 10

n(1-p) 10 1749(.728) 10

3.pop 10 n 3.pop 10(1749)

1-Proportion Z-TestHo: p=.272

Ha: p .272

Z= = -1.9198

2*P(z<-1.9198)=.054879

npp

pp

)1(

ˆ

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 1.assumed

2.Normal population 2.34 30

or

n 30

T-Test of Marshmallow Weight

25137.)1675.1(2

1675.1

1087.13:

1087.13:

tPns

xt

Ha

Ho

34

6562.12

n

x

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

27^107987.2)041984.8(2

041984.8

49:

49:

tPns

xt

Ha

Ho

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

)775.52,251.51()(* nstx

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

z-test• 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