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

2. 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

3. 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

4. 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

5. 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

6. Bar Graph of Observed Values

7. Pie Graph of Observed Values

8. 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.

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

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

11. Chi-Square Goodness of Fit Test
Conclusion:
We reject Ho in favor of Ha because our p-value of 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.

12. 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

14. Male vs. Female Color Choice

15. 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

16. Chi-Square Association Test
Calculations:
2 = ∑(Observed –expected) 2 = ( )2 + ( )2 +…= Expected
2=
P(2 > |df= 5) =

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

18. 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

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

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

21. 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

22. 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

23. 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