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?
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?
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
Related questions
Question
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)
ANOVA
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.
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