1. By Josh Spiezle, Emy Chinen, Emily Lopez, Reid Beloff

2.  Do peanut M&M’s have the same % of color proportions as milk chocolate M&M’s?

3.  Well, we chose this as our final project because our group has Em and Em in it, and we all LOVE chocolate. Clearly, this made the most sense!

4.  Milk Chocolate M&M’s and Peanut M&M’s

5.  56 ounces of each kind!

6.  We will be counting out each color in the bag then divide by the total number of M&M’s in the bag.

7.  Ho: The proportions of colors in peanut M&M’s matches the proportions of the milk chocolate M&M colors.  Ha: At least one of the color proportions between the 2 types of M&M’s are not equal.

8.  1.) Randomness – bags of each type of M&M’s chosen randomly

9. 2.)Expected values are greater than 5 Observed (Regular)Peanut (Becomes E)Expected(O-E)² /(E) Red249139141.7181.2301 Orange391314320.12515.6916 Yellow195384391.4998.6189 Green267348354.7921.7229 Blue462296301.7785.0769 Brown213262267.1110.9614 Total177717431777χ² = 313.3018

10. 3.) Independence Since we are sampling without replacement, must check 10% condition. N p = 10n p » N p = 10(1743) » N p = 17430 N R = 10n R » N R = 10(1777) » N R = 17770 Safe to assume at least 17,430 peanut M&M’s and 17,770 milk chocolate M&M’s in entire population so 10% condition is met.

11. X ² -Homogeneity test! df = (r-1)(c-1) = (6-1)(2-1) = 5 X² cdf (313.3018, 1000, 5) X² -value large # df P-value = 1.38131x 10^-65 Color of M& M (O-E)² /(E) Red 81.2301 Orange 15.6916 Yellow 98.6189 Green 21.7229 Blue 85.0769 Brown 10.9614 ∑ = χ² = 313.3018

13.  Type I-Statistical test rejects that proportions of colors are equal when they are.  Type II-Statistical test fails to reject them being equal when they are not.  We believe that neither error type is worse in this situation so we will be leaving our alpha level at 0.05.

14.  Our Chi-Squared Test of Homogeneitygives a p-value of 1.382 x 10^-65 which is significantly less than any reasonable alpha level. Thus we are able to reject our null hypothesis and conclude there is enough evidence to say that the proportion of the colors in peanut M&M’s and milk chocolate M&Ms are not equal.

15.  Plain Variety:  30% brown  20% yellow  20% red  10% green  10% orange  10% blue  Peanut Variety:  20% brown  20% yellow  10% red  10% green  10% orange  30% blue