The experiment was conducted to compare four different pre-planting treatments for soy- bean seeds. The fourth treatment, consisting of not treating the seeds, was used as a control. The experimental area consisted of three fields. The soil scientist acknowledged some differences in the fields with respect to soil fertility and slope of land. Therefore, each field was divided into four plots and one of the treatments was randomly assigned to a plot within each field. The measurements are the number of plants which failed to emerge out of 100 seeds planted per plot. The data is given here. Field Treatment 1 2 3 Avasan 2 5 8 Spergon 4 8 9 Semasan 3 6 9 Control 8 10 12 Field Mean 4.25 7.25 9.5 Treatment Mean 5 7 6 10 7 a. Give an appropriate model to analyze this data, and state the assumptions. b. Given SSrotal = 100, test if the treatments have different effects. To get full credits, give the hypotheses, test statistic, p-value (or range of p-value) and your conclu- sion (use a = 0.05). (Hint: you need to first calculate sums of squares and then construct the test staristic.) (df ,dfa) (2,5) (3,5) (4,5) (2,6) (3.6) Fo.021 / 8.4336 77636 7.3879 7.2599 6.5988 6.2272 Food 5.7861 5.4095 5.1922 5.1433 4.7571 4.5337 c. Use Tukey's method to perform pairwise comparison of the distances with a 0.05) and report your results. 5 90.000;4f14 90.00 / (46) 515580 511579 6.25675.7717 4.6017 4.3392 5.2183 4.8956