Are there equal numbers of the different colors of M&Ms; in a package. Data was

Question

Are there equal numbers of the different colors of M&Ms; in a package. Data was collected to answer this question, use the output below to answer the following questions: 1. Looking at the plots, describe the comparison of number of M&Ms; of the different colors. 2. To test if there is a difference in the number of M&Ms; between the colors, we run ANOVA. Why should we use ANOVA and not a t-test? 3. Is it reasonable to pool the standard deviations (variances)? Why? Why do we care whether it is reasonable to pool the standard deviations? 4. What are the hypotheses for your test? 5. What are the test statistic and P-value for your hypotheses? In terms of the problem, what is your conclusion? 6. Based on your results, do you need to analyze your data further? If so, what procedure should you use?

Explanation / Answer

1) we see the line polt with crets and trough , hence the mean values appear to be different , atleast visually

2) we would run aanova when we have more than 2 groups for comparison . we run t test when we ahve to compare the mean values of 2 groups only

4) Hypothesis test
H0: There is no difference in the number of M&Ms between the colors
H1: There is a statistical difference in the number of M&Ms between the colors , atleast for 2 colors
5) we see that the p value is less than 0.0001 , hence the result is statistially significant , considering an alpha = 0.05, hence we conclude that
H1: There is a statistical difference in the number of M&Ms between the colors , atleast for 2 colors

we reject null hypothesis in favor of alternate hypothesis

6) remember anova is an omnibus test , it only tells whether the mean values are same or different across groups , it doesnt tell which groups are different statistically. hence in order to do so , we would run a post hoc analysis such as a tukeyhsd test

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