Question

Mars, Inc. candy company claims the overall proportions for the colors of M&M’s are: .24 blue, .13 brown, .20 green, .16 orange, .13 red, and .14 yellow. You buy a large bag of M&M’s and observe the following counts: 105 blue, 72 brown, 89 green, 84 orange, 70 red, 80 yellow. At the 0.05 level of significance, is there evidence that the overall proportions for the colors are as stated above?

Answer 1

There is insufficient statistical evidence to prove that the companies stated color distribution is not correct therefore, the overall proportions of the colors are correctly stated as above

Explanation:

We have that

H₀: 0.24 blue, 0.13 brown, 0.20 green, 0.16 orange, 0.13 red and 0.14 yellow

The Data given are as follows;

Hₐ: The stated distribution of M&M is incorrect

Blue Brown Green Orange Red Yellow Total

Observed: 105 72 89 84 70 80 500

Expected: 120 65 100 80 65 70

We have;

`\chi ^(2)=(\left (105-120 \right )^(2))/(120)+ (\left (72-65\right )^(2))/(65) + (\left (89-100\right )^(2))/(100) + (\left (84-80\right )^(2))/(80) + (\left (70-65\right )^(2))/(65) + (\left (80-70\right )^(2))/(70) = 5.85`

At 6 - 1 = 5 degrees of freedom we find the p-value from the chi squared table as follows

P(0.05) at 5% degrees of freedom =11.070 hence our P-value is larger than 0.05 and we fail to reject the null hypothesis, hence there is insufficient statistical evidence to prove that the companies stated color distribution is not correct.