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# Project on M&M's

M&Ms has more recently updated its color distribution pattern to Red: 13%, Yellow: 14%, Green: 16%, Orange 20%, Blue: 24%, Brown: 13%.

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Perform hypothesis tests (at a 5% level of significance) to determine:

1. Are the class total proportions representative of the current (updated) listed proportions?

2. Which, if any, of the six groups had proportions that are representative of the current (updated) proportions?

3. Which, if any, of the six groups had proportions that are representative of the CLASS proportions?

4. Test your personal M&M sample. was it representative of the CLASS proportions?

Since much of the setup within each question is repetitive, you do not need to repeat all 5-steps completely for each group individually, but make sure to clearly identify the type of test, your null and alternative hypotheses for each question, the critical value, and show (in Excel) or explain (on the calculator) the calculation of your test statistics. Answer the original questions with supported conclusions.

#4 must show all 5 steps of the Hypothesis test for full credit. Make sure you include your data.

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DATA:

Our class totals for the colors are:

Red: 524, Yellow: 519, Green: 676, Orange: 841, Blue: 802, Brown: 507

My personal data are:

Red Yellow Green Orange Blue Brown Total
Yours 16 15 23 30 20 15 119

(See attachment for the complete data set.)

#### Solution Preview

Please see the work in the attached Excel file. Let me know if you have any questions!

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1. Are the class total proportions representative of the current (updated) listed proportions?

(1) This test will determine if the M&M's from the class data have a different color distribution than the updated proportions. A chi-square goodness of fit test will be used.

(2) Hypotheses:
Null hypothesis (H0): the class data is consistent with the listed distribution.
Alternative hypothesis (Ha): the class data is not consistent with the listed distribution

(3) The chi-square statistic is calculated as X2 = sum of (observed - expected)2/expected.

X2 = (524- 502.97)2/502.97 + (519 - 541.66)2/541.66 + (676 - 619.04)2/619.04 + (841 - 773.8)2/773.8 + (802 - 928.56)2/928.56 + (507 - 502.97)2/502.97
X2 = 0.879298765 0.947966621 5.241085552 5.835926596 17.24975618 0.032289997
X2 = 30.18632371

(4) The critical value for a chi-square test with 5 degrees of freedom (at the 0.05 significance level) is X2 = 11.070 (see ...

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