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 BGrain A163163287287305305267267304304325325198198348348172172Grain B338338291291223223286286168168309309321321173173189189Grain C202202299299318318219219291291252252261261358358312312Grain D175175161161208208199199307307342342272272208208268268 ANOVASource of VariationSSSSdfdfMSMSGrain7974.30567974.3056332658.10192658.1019Grass5302.88895302.8889222651.44452651.4445Interaction46651.777846651.7778667775.29637775.2963Within72575.333372575.333324243023.97223023.9722Total132504.3056132504.30563535 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. Round your answer to two decimal places, if necessary.

Given that,The dependent variable is the weight gain of his cows.The weight gain of cows depends on…

Answered: Is there sufficient evidence to…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.CR: Chapter 1 Review

Problem 78CR

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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 A	Grass B	Grass B
Grain A	163163	287287	305305
267267	304304	325325
198198	348348	172172
Grain B	338338	291291	223223
286286	168168	309309
321321	173173	189189
Grain C	202202	299299	318318
219219	291291	252252
261261	358358	312312
Grain D	175175	161161	208208
199199	307307	342342
272272	208208	268268

ANOVA

Source of Variation	SSSS	dfdf	MSMS
Grain	7974.30567974.3056	33	2658.10192658.1019
Grass	5302.88895302.8889	22	2651.44452651.4445
Interaction	46651.777846651.7778	66	7775.29637775.2963
Within	72575.333372575.3333	2424	3023.97223023.9722
Total	132504.3056132504.3056	3535

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. Round your answer to two decimal places, if necessary.

Expert Solution