A random sample of 33 individuals is selected from a population, and these individuals are then randomly assigned to 3 treatment groups (such that each group has an equal number of individuals).

The following ANOVA table summarizes the results of measurements taken from each individual, within each group, on a characteristic of interest. Due to the small p-value, the null hypothesis is rejected, and at least one of the treatments means is different.

Source S SS MS p - value Groups 2 064.59 032. 295 8.560535 0.001 144 Error 20 3 . 617 63 20 5876 67 Total 32 5. 682 . 22 The sample means for each of the treatment groups were found to be a 2186 , 12 - 19.54 , and Ing = 10.68 Use Fisher's Least Significant Difference ( LSD ) method to carryout pairwise comparisons between the treatment means , and determine which means are different . a ) What is the value of the standard error of the difference in treatment means , SE ( X X 3 ) ? Round your response to at least 3 decimal places ) What are the appropriate degrees of freedom for the i distribution used to find to ? ( ) Deter mine whether or not there is significant evidence of a difference between each pair of treatment means , at the 5 % level of significance