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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-VarietyRedGreenBlueOrangeBrownYellowTotals: Totals:

Variety-2006 M&M stats from siteProportions Totals (proportions*1068) Red13% Green16% Blue24% Orange20%213.6 Brown13% Yellow14% Total100%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: 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 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=  The degrees of freedom=(# categories-1) =(6-1)=5  The p-value=  2cdf( ,99999,5) =

 M&M’s® Charts that show Color Proportions

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

 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 % 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.

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