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By: Rochelle Cooper, Jon Hale, and Ainsley Hume

By: Rochelle Cooper, Jon Hale, and Ainsley Hume. Lucky Charms, A History. 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

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By: Rochelle Cooper, Jon Hale, and Ainsley Hume

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  1. By: Rochelle Cooper, Jon Hale, and Ainsley Hume

  2. Lucky Charms, A History • 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

  3. 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

  4. 62.9g 65.89 61.28g 71.73g 63.89g 60 62 64 66 68 70 72 74 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

  5. 62.9g 65.89 60 62 64 66 68 70 72 74 61.28g 68.04g 71.73g 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

  6. 19 .276 .146 .377 .242 .1 .2 .3 .4 Boxplot for proportion of marshmallows in Lucky Charms Mini Boxes • 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

  7. 11 Frequency 0 .14 .16 .18 .2 .22 .24 .26 .28 .3 .32 .34 .36 .38 -6 Proportion of Marshmallows Histogram for proportion of marshmallows in Lucky Charms Mini Boxes • X-axis:proportion of marshmallows • Y-axis:frequency • Right skewed • =.24 • Range=.24

  8. 25 20 15 Marshmallow total weight in grams 10 5 40 45 50 55 60 65 Mini Boxes total Weight in grams Scatterplot for proportion of marshmallows in Lucky Charms Mini Boxes • Slightly positive direction • Moderately weak • Linear

  9. 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) Passed!

  10. 1-Proportion Z-Test Ho: p=.272 Ha: p .272 Z= = -1.9198 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.

  11. Assumptions for T-Test of Marshmallow Weight 1.SRS 1.assumed 2.Normal population 2.34 30 or n 30 Passed!

  12. 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 13.1087 grams.

  13. 1.SRS 1.assumed 2.Normal population 2.34 30 or n 30 Assumptions for T-Test of Serving Size Weights Passed!

  14. 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.

  15. Confidence Interval We are 95% confident that the mean serving size weight is between 51.251 and 52.775 grams.

  16. 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

  17. 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.

  18. 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

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