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

Ho : P1 = 0.2, P2 = 0.2, P3 = 0.2, P4 = 0.2, P5 = 0.2 Ho: Some of the population proportions differ from the values stated in the null hypothesis

Expected value = 60/5 = 12

Categories Observed Expected (fo-fe)?/fe Category 1 8 60*0.2=12 Category 2 14 60*0.2=12 20 60*0.2=12 Category 3 Category 4 (8-12)2/12 = 1.333 (14-12)2/12 = 0.333 (20-12)2/12 = 5.333 (10-12)2/12 = 0.333 (8-12)2/12 = 1.333 10 60*0.2=12 Category 5 8 60*0.2=12 Sum = 60 60 8.667

Based on the information provided, the significance level is a = 0.05, the number of degrees of freedom is df = 5-1=4, so then the rejection region for this test is R= {x? : x² > 9.488).

n x = (0; – E;) E; = 1.333 + 0.333 +5.333 + 0.333 + 1.333 = 8.667 i=1

Since it is observed that x = 8.667 <x< = 9.488, it is then concluded that the null hypothesis is not rejected.

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is NOT enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the a = 0.05 significance level.