Data on the butterfat content of milk from Canadian cows of five different breeds can be found in the butterfat dataset (in Faraway R package). Consider only mature cows.

(a) Produce a Boxplots depicting the data and interpret what you see.

(b) Perform a one-way ANOVA with Butterfat as the response and Breed as the predictor variable and test using the 5% level of significance for a difference among the breeds. For the test provide the null and alternative hypotheses, critical region, test statistic and your conclusion.

(c) Check the regression diagnostics commenting on any violations.

(d) Check for significant pairwise differences in butterfat between breeds. Which pairs are significantly different at 5% level? For the test provide the null and alternative hypotheses, critical regions, test statistic and your conclusion.

Present your R codes used to answer the question.