a dairy farmer thinks that the average weight gain of his cows depends on two factors: the type of grain that they are fed and the type of grass that they are fed. the dairy farmer has four different types of grain from which to choose and three different types of grass from which to choose. he would like to determine if there is a particular combination of grain and grass that would lead to the greatest weight gain on average for his cows. he randomly selects three one-year-old cows and assigns them to each of the possible combinations of grain and grass. after one year he records the weight gain for each cow (in pounds) with the following results. is there sufficient evidence to conclude that there is a significant difference in the average weight gains among the cows for the different types of grain? cow weight gain (pounds) grass agrass bgrass b grain a172182275 284192174 175284181 grain b204255275 206277342 184225250 grain c356186291 264360353 225315285 grain d267289172 212317271 319252192 anova source of variationssdfms grain28833.194439611.0648 grass3148.166721574.0834 interaction19801.388963300.2315 within68544.0000242856.0000 total120326.750035 step 1 of 2 : find the value of the test statistic for testing the difference in average weight gains among the cows for the different types of grain