A farmer is comparing three different types of fertilizer which are Type 1 (Column 1), Type 2 (Column 2) and Type 3 (Column 3). He would like to determine whether the types of fertilizer differ with respect to final crop yield (in bushels per acre). He randomly assigned different number of samples size for the three groups. Their final crop yield are compared at the end period of experiment. An alpha criterion of 0.05 were used for the test. The OUTPUT 1 represent the results for analysis of variance (ANOVA) using SPSS. The sample dataset from our imaginary crop yield experiment contains data about:fertilizer type (type 1, 2, or 3)final crop yield (in bushels per acre)By referring to the SPSS OUTPUT 1, answer the following questions:What was the purpose of the study? How many treatment groups were used in the study? What is the variable that used to find the means (average) in SPSS OUTPUT 1? What was the sample size?In one way ANOVA procedure, all populations have to follow what distribution?What may have been the hypothesis for the one way ANOVA procedure in the study?Why was the one way ANOVA procedure used, as opposed to another test, such as independent sample t test?At 5% level of significance, what is your conclusion about the hypothesis in Question 6?Do we need the Tukey post-hoc test to analyze the data in this study? Justify. Multiple ComparisonsDependent Variable: YieldTukey HSDMean Difference95% Confidence Interval(1) Fertilizer(J) Fertilizer(I-J)Std. ErrorSig.Lower BoundUpper Bound12-176.155.495-55.19-599155.001-97-.2321.176155.495-19.553-423.155.021-79-.0531599.155.00123.972.423155.021.0579*. The mean difference is significant at the 0.05 level. SPSS OUTPUT 1DescriptivesYield95% Confidence Interval forMeanNMeanStd. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum132176.76.685.121176.51177.0017517832176.93574.101176.73177.1417617832177.36599.106177.14177.57176179Total96177.02.665.068176.88177.15175179ANOVAYieldSum of SquaresMean SquaredfFSig.Between Groups6.06823.0347.863.001Within Groups35.88693.386Total41.954952.3,

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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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A farmer is comparing three different types of fertilizer which are Type 1 (Column 1), Type 2 (Column 2) and Type 3 (Column 3). He would like to determine whether the types of fertilizer differ with respect to final crop yield (in bushels per acre). He randomly assigned different number of samples size for the three groups. Their final crop yield are compared at the end period of experiment. An alpha criterion of 0.05 were used for the test. The OUTPUT 1 represent the results for analysis of variance (ANOVA) using SPSS.

The sample dataset from our imaginary crop yield experiment contains data about:

fertilizer type (type 1, 2, or 3)
final crop yield (in bushels per acre)

By referring to the SPSS OUTPUT 1, answer the following questions:

What was the purpose of the study?
How many treatment groups were used in the study?
What is the variable that used to find the means (average) in SPSS OUTPUT 1?
What was the sample size?
In one way ANOVA procedure, all populations have to follow what distribution?
What may have been the hypothesis for the one way ANOVA procedure in the study?
Why was the one way ANOVA procedure used, as opposed to another test, such as independent sample t test?
At 5% level of significance, what is your conclusion about the hypothesis in Question 6?
Do we need the Tukey post-hoc test to analyze the data in this study? Justify.

Multiple Comparisons
Dependent Variable: Yield
Tukey HSD
Mean Difference
95% Confidence Interval
(1) Fertilizer
(J) Fertilizer
(I-J)
Std. Error
Sig.
Lower Bound
Upper Bound
1
2
-176
.155
.495
-55
.19
-599
155
.001
-97
-.23
2
1
.176
155
.495
-19
.55
3
-423
.155
.021
-79
-.05
3
1
599
.155
.001
23
.97
2
.423
155
.021
.05
79
*. The mean difference is significant at the 0.05 level.

SPSS OUTPUT 1
Descriptives
Yield
95% Confidence Interval for
Mean
N
Mean
Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum
1
32
176.76
.685
.121
176.51
177.00
175
178
32
176.93
574
.101
176.73
177.14
176
178
32
177.36
599
.106
177.14
177.57
176
179
Total
96
177.02
.665
.068
176.88
177.15
175
179
ANOVA
Yield
Sum of Squares
Mean Square
df
F
Sig.
Between Groups
6.068
2
3.034
7.863
.001
Within Groups
35.886
93
.386
Total
41.954
95
2.
3,

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