By: Avni Choksi and Brittany Nguyen M&M’s By: Avni Choksi and Brittany Nguyen

History Forrest Mars visited Spain during Spanish Civil War and encountered soldiers eating chocolates in hard sugary coating Inspired because chocolates didn’t melt M&Ms were first sold in cardboard tubes during WWII for soldiers In 1995, vote for new color-blue, pink, or purple…blue won by a landslide

Purpose To determine if color affects the choice of M&M consumption To determine if gender is associated with M&M color choice To test the claim that more than 16.7% of our subjects will choose the blue M&M

What We Did Randomly chose 6 CB south classes using calculator Placed 50 of each color (blue, red, orange, green, brown, yellow) into a container Asked each student to pick which color M&M they wanted Refilled container after each class so that the proportion of each color was always the same

Does M&M color affect consumption? Table of Observed Values M&M Color Blue Red Orange Brown Green Yellow Frequency of observed values 43 24 12 11 22 14

Bar Graph of Observed Values

Pie Graph of Observed Values

Chi-Square Goodness of Fit Test Assumptions: SRS All expected counts are greater than or equal to 5 Check: Randomly picked classrooms using calculator All of the expected counts are greater than or equal to 5 Hypotheses: Ho: the observed distribution of the choice of M&M color fits the expected distribution. Ha: the observed distribution of the choice of M&M color does not fit the expected distribution.

Chi-Square Goodness of Fit Test Expected Values: n=126 Expected values= 126/6 colors = 21

Chi-Square Goodness of Fit Test Calculations: 2 = ∑(Observed –expected) 2 = (43-21)2 + (24-21)2 +…= 34.37 Expected 21 21 P(2 > 34.37|df= 5) = 1.9138 x 10-6

Chi-Square Goodness of Fit Test Conclusion: We reject Ho in favor of Ha because our p-value of 1.9138 x 10-6 < α =0.05. We have sufficient evidence that the observed frequency distribution in the color consumption of M&M’s does not fit the expected distribution.

Does Gender affect M&M Color Consumption? Table of Observed Values: Gender vs. Color Choice Color Blue Red Orange Brown Green Yellow Male 26 17 6 10 13 4 Female 22 7 1 9

Male vs. Female Color Choice

Chi-Square Association Test Assumptions: SRS All expected counts are greater than or equal to 5 Check: Randomly picked classrooms using calculator All of the expected counts are not greater than or equal to 5 but we still proceed with the test Hypotheses: Ho: Gender and color consumption of M&M’s are independent Ha: Gender and color consumption of M&M’s are dependent

Chi-Square Association Test Calculations: 2 = ∑(Observed –expected) 2 = (26-27.847)2 + (17-13.924)2 +…= Expected 21 2= 12.1071 P(2 > 12.1071|df= 5) = 0.03335

Chi-Square Association Test Conclusion: We reject Ho in favor of Ha because our p-value of 0.03335 is <α 0.05. We have sufficient evidence that the gender and M&M color consumption are dependent

One Proportion Z-Test Assumptions:  Hypotheses: Independent SRS n(p) ≥ 10 n(1-p) ≥ 10 pop ≥ 10 * n Hypotheses: Ho: p=1/6 picked blue Ha: p>1/6 picked blue Check -Randomly picked classrooms using calculator (126)(1/6) (126)(5/6) - pop≥ 1260  ≥ 10

One Proportion Z-test Calculations: z= = 5.259 P(z>5.259)= 7.2564 x 10-8

One Proportion Z-test Conclusion: We reject Ho in favor of Ha because our p-value of 7.2564 x 10-8 <α= 0.05. we have sufficient evidence that the proportion of those that pick blue is greater than 0.167.

Potential Sources of Bias/Error Only covers a few high school classes Leaves out younger/older age range Response bias- our presence could have affected the subject’s choice Sample Method – we didn’t randomly sample each individual, but chose the classroom as a whole Voluntary response – from the teachers Balance of color – might cause people to pick the more abundant color, since we didn’t refill after each pick

Personal Opinion We conclude that color does affect M&M consumption Blue was much more popular than the other colors since we believe that it is more attractive to the human eye Brown and orange were the least picked colors because their earthy tones are not as vibrant Males tended to choose more masculine colors, such as red and brown Females tended to choose more feminine colors, such as yellow, and tended to stay away from brown

Application We counted the amount of M&Ms in 2 bags, and found that there were 162 blue 95 green 84 orange 67 yellow 43 red 38 brown We believe that M&M companies put more blue in their bags since it is the most attractive color