The M&M’s® Experiment

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Are the proportions of colors of each M&M stated by the M&M company true proportions?

Convenience Sampling ◦ Randomly chosen from store’s bin of M&M’s®

20 bags of M&M's®

Package-Variety Red Green Blue Orange Brown Yellow Totals:

1 5 11 8 10 13 7 542 8 12 4 6 10 14 543 11 9 4 10 10 10 544 6 8 6 15 11 9 555 6 12 8 6 9 13 546 8 11 6 14 7 9 557 10 14 5 8 8 9 548 11 9 3 12 9 10 549 5 9 5 14 10 11 5410 6 12 8 6 10 8 5011 8 10 5 11 7 13 5412 5 14 3 11 15 6 5413 3 13 5 11 9 13 5414 5 12 6 13 9 9 5415 5 12 4 15 9 10 5516 6 11 10 10 6 10 5317 8 11 5 8 2 10 4418 6 12 5 13 12 6 5419 9 12 4 13 8 8 5420 6 11 5 14 10 8 54

Totals: 137 225 109 220 184 193 1068

Raw Data (Observed)

Raw Data (Expected)Variety-2006 M&M stats from site Proportions

Totals (proportions*1068)

Red 13% 138.84

Green 16% 170.88

Blue 24% 256.32

Orange 20% 213.6

Brown 13% 138.84

Yellow 14% 149.52

Total 100% 1068

Ho: Observed=Expected◦ The count of M&M’s® for each color that we

observed in our sample of 20 bags of M&M’s® is the same as the count of M&M’s® stated on the M&M’s® main website.

Ha: ObservedExpected◦ The count of M&M’s® for each color that we

observed in our sample of 20 bags of M&M’s® is not the same as the count of M&M’s® stated on the M&M’s® main website.

Using the Chi-squared Test for Goodness of Fit, since all counts are greater than 5, we can carry out a Test for Goodness of Fit. We shall proceed with caution since this is a convenience sample.

The test statistic 2=129.3617928 The degrees of freedom=(# categories-1) =(6-1)=5 The p-value=2cdf(129.3617928,99999,5)=0.000000000000000000000000032509

M&M’s® Charts that show Color Proportions

Red13%

Green21%

Blue10%Orange

21%

Brown17%

Yellow18%

M&M's® Colors (Observed Pro-

portions)

mRed13%

Green16%

Blue24%

Orange20%

Brown13%

Yellow14%

M&M's® Colors (Expected Proportions)

m

Bar Graphs that show the Counts of M&M’s® Color per Bag

(continued)

M&M's Colors (Observed)

Red Green Blue Orange Brown Yellow0

50

100

150

200

250

Observed Count of each M&M's Color in 20 Bags

M&M's® Color

Num

ber O

bser

ved

Red Green Blue Orange Brown Yellow0

50

100

150

200

250

Expected Count of each M&M's Color in 20 Bags

M&M's® Color

Num

ber E

xpec

ted

At a 1% significance level, (99% confidence level), we must reject the null hypothesis.

In conclusion, with the present data, assuming that this is a SRS rather than simply a convenience sample, we must conclude that the 2009 sample has a 0.0000000000000000000000032509% of occurring if the 2006 proportions is true, therefore since the probability is less than 1%, there is enough evidence to show that the 2006 proportion expected by the company is false.

Possible bias include:◦ Convenience Sampling Bias

Since the data was not derived from a SRS, but was taken from a convenient random drawing of M&M’s® packets from the local store, there may be some non-response bias. This type of bias can be prevented if a random sample of one M&M’s® at a time is taken from all M&M’s® factories in the world.

Due to the convenience sampling, the count for blue M&M’s may be significantly higher than expected. In addition, other abnormities in the count per color may be accounted due to the convenience sampling.

Good luck in finishing statistics, and we look forward to looking at your projects!

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