According to Mars Inc., the distribution of colors of the M&M candies is Brown- 13 Yellow- 14 Red- 13 Blue- 24 Orange- 20 Green-. 16.Several bags were randomly chosen and the percentages of each color were found to be as follows: Brown – 15.3%, Yellow –18.1%, Red – 11.7%, Blue – 19.8%, Orange – 22.6%, and Green – 12.5%. According to this sample, does it appear that the distribution of colors does not fit what’s expected, according to the manufacturer’s percentages?
State your hypotheses, test statistic, p-value, and conclusion (in terms of the problem).
Solve using Ti-83 or 84
The null and alternate hypothesis are:
H0: Distribution of colors is according to the manufacturer's
percentages.
Ha: Distribution of colors is not according to the manufacturer's
percentages.
Now, Expected frequency = [(Row total) x (Column total)] / Table total
So,
Color | Oi | Ei | |
Brown | 15.3 | 13 | |
Yellow | 18.1 | 14 | 2.0008 |
Red | 11.7 | 13 | 0.13 |
Blue | 19.8 | 24 | 0.735 |
Orange | 22.6 | 20 | 0.338 |
Green | 12.5 | 16 | 0.7656 |
Total | 4.3763 |
Test statistic value =
The critical value is given by:
Since the test statistic value is less than the critical value, so
we do not have sufficient evidence to reject null hypothesis H0.
Thus, we can say that the distribution of colors is according to
the manufacturer's percentages.
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