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 4646 4747 4444 North Side 4545 5050 4848 West Side 4646 4949 4040 East Side 5252 6060 5252 Copy Data ANOVA Source of Variation SSSS dfdf MSMS Rows 176.2500176.2500 33 58.750058.7500 Columns 66.500066.5000 22 33.250033.2500 Error 35.500035.5000 66 5.91675.9167 Total 278.2500278.2500 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.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.4: Collecting Data

Problem 2E

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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	4646	4747	4444
North Side	4545	5050	4848
West Side	4646	4949	4040
East Side	5252	6060	5252

Copy Data

ANOVA

Source of Variation	SSSS	dfdf	MSMS
Rows	176.2500176.2500	33	58.750058.7500
Columns	66.500066.5000	22	33.250033.2500
Error	35.500035.5000	66	5.91675.9167
Total	278.2500278.2500	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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