1. The Original Box Cox (30 points total) A commonly used transformation in statistics (which we won't be using here) is the Box-Cox transform. The original 1964 article by George Box, and David Cox1 that described this method used a data set that has shown up in several statistics articles since2,3. The data are survival times of rats that were given one of three poisons. The results are summarized as follows Table 1: Survival times (unit, 10hr) of rats after poison administration Poison1 Poison 2 Poison 3 0.36 0.29 0.40 0.23 0.92 0.61 0.49 1.24 0.44 0.35 0.31 0.40 0.56 1.02 0.71 0.38 0.31 0.45 0.46 0.43 0.82 1.10 0.88 0.72 0.43 0.45 0.63 0.76 0.45 0.71 0.66 0.62 0.22 0.21 0.18 0.23 0.30 0.37 0.38 0.29 0.23 0.25 0.24 0.22 0.30 0.36 0.31 0.33 a) What are the null and alternative hypotheses? (b) Fill in the following one-way ANOVA table, assume = 0.05 and make a conclusion. Make sure to use the formula covered during the lecture on one-way ANOVA. Table 2: Analysis of variance of survival times (unit, 10hr) of rats after poison administration Source of Variation DOF Sum Sq (SS Mean Sq (MS) F valueFa Poison Error Total (c) sing Tukey's honestly significant difference method determine the confidence interval (CI) of each difference by filling the following table. Which groups are significantly different? Table 3: Post-hoc analysis of survival times (unit, 10hr) of rats after poison administration Poison A Poison B CI Lower Bound Difference in Means CI Upper Bound 2 (d) Use MATLAB's anoval function to make a conclusion. Make sure to include the table and the figure. Compare the table calculated by anoval command and the one from Part (1b) (e) Use MATLAB's multcompare function to get the confidence interval table. Compare it significantly different from each other. Also, include figure outputs from multcompare. with the one from Part (1c). Based on the confidence interval table, find which groups are