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 Side of Farm Fertilizer A Fertilizer B Fertilizer C South Side 4747 5656 5050 North Side 5555 4444 4848 West Side 5353 5454 6060 East Side 4848 5454 5757 Copy Data ANOVA Source of Variation SSSS dfdf MSMS Rows 73.000073.0000 33 24.333324.3333 Columns 18.166718.1667 22 9.08349.0834 Error 156.5000156.5000 66 26.083326.0833 Total 247.6667247.6667 1111 Copy Data Step 1 of 3 : 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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

Side of Farm	Fertilizer A	Fertilizer B	Fertilizer C
South Side	4747	5656	5050
North Side	5555	4444	4848
West Side	5353	5454	6060
East Side	4848	5454	5757

Copy Data

ANOVA

Source of Variation	SSSS	dfdf	MSMS
Rows	73.000073.0000	33	24.333324.3333
Columns	18.166718.1667	22	9.08349.0834
Error	156.5000156.5000	66	26.083326.0833
Total	247.6667247.6667	1111

Copy Data

Step 1 of 3 :

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.

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