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 Q 1 =62.9g Median=63.89g Q 3 =65.89g Max=71.73g IQR=Q 3 -Q 1 =(65.89g)-(62.9g)=2.99g g 71.73g 62.9g g

Outliers for initial weight of Lucky Charms Mini Boxes IQR=Q 3 -Q 1 =(65.89g)-(62.9g)=2.99g Outlier test  Q 3 +[IQR(1.5)]=High limit:70.375g  Q 1 -[IQR(1.5)]=High limit:70.375g  1 outlier: #25, 71.73g g 68.04g 71.73g 62.9g g

Min.=.1456 Q 1 =.1898 Median=.2421 Q 3 =.2464 Max=.3777 IQR=Q 3 -Q 1 =(.2464)-(.1898)=.0566 Outlier test  Q 3 +[IQR(1.5)]=High limit:  Q 1 -[IQR(1.5)]=High limit:  No outliers Boxplot for proportion of marshmallows in Lucky Charms Mini Boxes

Histogram for proportion of marshmallows in Lucky Charms Mini Boxes X-axis:proportion of marshmallows Y-axis:frequency Right skewed =.24 Range= Proportion of Marshmallows

Mini 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 (.272) 10 n(1-p) (.728) 10 3.pop 10 n 3.pop 10(1749)

1-Proportion Z-Test Ho: p=.272 Ha: p.272 Z= = *P(z< )= 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 or n 30

T-Test of Marshmallow Weight We fail to reject the Ho because p>.05=. We have sufficient evidence that the mean marshmallow weight is equal to grams.

Assumptions for T-Test of Serving Size Weights 1.SRS 1.assumed 2.Normal population or n 30

T-Test of Serving Size Weights 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 We are 95% confident that the mean serving size weight is between and 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, 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