Question

M&Ms/Mars Company, the maker of Skittles, state that each bag of Skittles has the same number of each flavor in it. Use 0.05 level of significance to test the company's claim. Below is the observed number in a bag of Skittles: Observed Flavors: Lime 8, Lemon 14, Orange 20, Strawberry 10, Grape 8 Expected Flavors: All the categories of flavors are the same.

Answer 1

Here, Total number of skittles = 8+14+20+10+8=60

Since the expected number of flavors of all the categories are same.

So, expected number of flavors for each category = 60/5=12

Here we test the following hypothesis.

H₀ :All the categories of flavors have the same amount in the bag of skittles.

H₁: Atleast one of the flavour categories doesnot have the same amount in the bag of skittles.

Here we perform the chi squared goodness of fit test.

The following table gives the obseved and expected number of candies for each flavor.

Flavors	Lime	Lemon	Orange	Strawberry	Grape
Observed	8	14	20	10	8
Expected	12	12	12	12	12

The chi square test statistic is given by,

1* = [ (0; – E:)! E;

Where is the observed value

O

and, is the expected value

E

$\chi^2=1.3334+0.3334+5.3334+0.3334+1.3334=8.667$

The critical value at level of significance is given by,

g= 0,05

$\chi_{\alpha,n-1}^2=\chi_{0.05,5-1}^2=\chi_{0.05,4}^2=9.488$

Since,

$\chi_{obs}^2<\chi_{\alpha,n-1}^2$

We fail to reject the null hypothesis at 0.05 level of significance.

CONCLUSION:

At the 0.05 level of significance all the categories of flavors have the same amount in the bag of skittles.

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