2. An investigation was conducted to determine the source of reduction in yield of a certain chemical product. It was thought that four different brands of a material may result in different yield reductions. The investigator assigned each brand of material randomly to 3 of the 12 batches of production of the chemical product. The following are the results of the percent of yield reductions: Percent of yield reduction Brand 1 Brand 2 Brand 3 Brand 4 25.6 25.2 20.8 31.6 24.3 28.6 26.7 29.8 27.9 24.7 22.2 34.3 Assume that all assumptions to perform an ANOVA test are satisfied. a) Test the hypothesis that the four brands have the same percent of yield reduction at the significance level, a = 0.05. Interpret the results of the hypothesis testing. b) Determine a 95% interval estimate for the percent of mean yield reduction of Brand 3. c) Determine a 99% interval estimate for the difference in the percent of mean yield reduction between Brands 4 and 3. (80 marks)