2. The tensile strength of Portland cement is being studied. Four different mixing techniques can be used economically. The following data have been collected: Technique Tensile strength 1 3129 3000 2865 2890 2 3200 3300 2975 3150 3 2800 2900 2985 3050 4 2600 2700 2600 2765 and can be read into R with the commands: y = c(3129 , 3000 , 2865 , 2890 , 3200 , 3300 , 2975 , 3150 , 2800 , 2900 , 2985 , 3050 , 2600 , 2700 , 2600 , 2765 ) x = c(rep(1,4),rep(2,4),rep(3,4),rep(4,4)) (a) Test the hypothesis that mixing techniques affect the strength of the cement. Use the one-way ANOVA model, assuming that the assumptions are met. Report the ANOVA table, including the pvalue, and your conclusion with a = .05. (b) Follow up the results above with i) a comparison between the rst and last mixing techniques and ii) a comparison between the average of the rst two techniques and the average of the last two techniques. Reports the estimates and conclusions for signicance. Use a Bonferroni adjustment so that the family-wise error rate does not exceed .05 for simultaneous interpretation