A banana grower has three fertilizers from which to choose. He would like to determine which fertilizer produces banana trees with the largest yield (measured in pounds of bananas produced). The banana grower has noticed that there is a difference in the average yields of the banana trees depending on which side of the farm they are planted (South Side, North Side, West Side, or East Side), therefore, a randomized block design is used in the study. Because of the variation in yields among the areas on the farm, the farmer has decided to randomly select three trees within each area and then randomly assign the fertilizers to the trees. After harvesting the bananas, he calculates the yields of the trees within each of the areas. Can the banana grower conclude that there is a significant difference among the average yields of the banana trees for the three fertilizers? The results are as follows. Average Yield of Banana Trees ANOVA Side of Farm Fertilizer A Fertilizer B Fertilizer C Source of Variation SS df MSSouth Side 47 56 50 Rows 73.0000 3 24.3333 North Side 55 48 48 Columns 18.1667 2 9.0834 West Side 53 54 60 Error 156.5000 6 26.0833 East Side 48 54 57 Total 247.6667 11 Step 1. Find the value of the test statistic for testing whether the average yield is the same for the three fertilizers. Round your answer to two decimal places, if necessary. (2 Points) Answer: F= Step 2. Make the decision to reject or fail to reject the null hypothesis that there is no difference among the average yields of the banana trees for the three fertilizers. State the conclusion in terms of the original problem. Use a = 0.05. (2 Points) A) We reject the null hypothesis. At the 0.05 level of significance, there is sufficient evidence of a difference among the average yields of the banana trees for the three fertilizers. B) We fail to reject the null hypothesis. At the 0.05 level of significance, there is not sufficient evidence of a difference among the average yields of the banana trees for the three fertilizers. Step 3. Was the banana grower able to significantly reduce variation among the observed yields by blocking? Use a = 0.05. (2 Points) A) The variation in yield is not significantly reduced by blocking since we fail to reject the null hypothesis that the block means are the same at the 0.05 level of significance. B) The variation in yield is significantly reduced by blocking since we reject the null hypothesis that the block means are the same at the 0.05 level of significance.
