Question

Researchers want to determine whether all bags of Skittles® have the same proportion of colors regardless of the flavor of Skittles®. To test this, they randomly sampled king-size bags of each flavor and recorded their findings in the table.

Below is a ctable

Flavor Skittles® Color Red Orange Yellow Blue Green

Original 15, 20, 18, 12, 16

Tropical 10, 7, 9 ,18 ,5

Wild Berry 16, 12, 13, 8, 10

Part A: What are the correct degrees of freedom for this table? (2 points)

Part B: Calculate the expected count for the number of blue tropical Skittles®. Show your work. (3 points)

Part C: Is there sufficient evidence that there is a difference in the proportion of colors for the different flavors of Skittles®? Provide a statistical justification for your conclusion. (5 points)

Answer 1

Solution:-

a)

DF = (r - 1) * (c - 1)

D.F = (5 - 1) * (3 - 1)
D.F = 8

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: There is no difference in the proportion of colors for the different flavors of Skittles.

Alternative hypothesis: There is difference in the proportion of colors for the different flavors of Skittles

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for homogeneity.

Analyze sample data. Applying the chi-square test for homogeneity to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.
E_r,c = (n_r * n_c) / n

b) Expected count for the number of blue tropical Skittles are 16 10 and 12.

Χ² = 13.9

where DF is the degrees of freedom, r is the number of populations, c is the number of levels of the categorical variable, n_r is the number of observations from population r, n_c is the number of observations from level c of the categorical variable, n is the number of observations in the sample, E_r,c is the expected frequency count in population r for level c, and O_r,c is the observed frequency count in population r for level c.The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 19.39.

We use the Chi-Square Distribution Calculator to find P(Χ² > 13.9) = 0.084

C) Interpret results. Since the P-value (0.084) is greater than the significance level (0.05), we failed to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that there is a difference in the proportion of colors for the different flavors of Skittles.