he following data shows the corn crop yield, in bushels per acre, categorized according to three varieties of corn (Variety 1, 2, 3) and three different soil types (Soil 1, 2, 3). Standard boxplot of corn crop yield (in bushels per acre) for each soil type and corn variety   a. What statistical test is most appropriate to answer this question? Identify the relevant assumptions and conditions and how these have or have not been met  b.Write an appropriate null and alterative hypothesis for this question.  c. What is the appropriate test statistic and what are their values? Please show any calculations. d. Assuming a 5% significance level, what is the appropriate decision for this test and why? f. Write a one-sentence conclusion statement.

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The following data shows the corn crop yield, in bushels per acre, categorized according to three varieties of corn (Variety 1, 2, 3) and three different soil types (Soil 1, 2, 3). Standard boxplot of corn crop yield (in bushels per acre) for each soil type and corn variety

 

a. What statistical test is most appropriate to answer this question? Identify the relevant assumptions and conditions and how these have or have not been met 

b.Write an appropriate null and alterative hypothesis for this question. 

c. What is the appropriate test statistic and what are their values? Please show any calculations.

d. Assuming a 5% significance level, what is the appropriate decision for this test and why?

f. Write a one-sentence conclusion statement. 

 

Researchers are interested in understanding if corn variety and soil type have an effect on corn
yield. For now, assume that yields are not affected by an interaction between variety and soil,
and test the null hypothesis that variety has no effect on yield and that soil type has no effect on
yield.
The appropriate test was performed in R. A portion of the results are shown below:
Df Sum Sq Mean Sq F value
2 1105.2
Pr (>F)
4.91e-05 ***
0.000616 ***
2 753.2
Residuals 31 1232.4
Variety
Soil
552.6
376.6
39.8
Transcribed Image Text:Researchers are interested in understanding if corn variety and soil type have an effect on corn yield. For now, assume that yields are not affected by an interaction between variety and soil, and test the null hypothesis that variety has no effect on yield and that soil type has no effect on yield. The appropriate test was performed in R. A portion of the results are shown below: Df Sum Sq Mean Sq F value 2 1105.2 Pr (>F) 4.91e-05 *** 0.000616 *** 2 753.2 Residuals 31 1232.4 Variety Soil 552.6 376.6 39.8
Sample Quantiles
10
5
0
-5
-10
-15
O
-2
yield
-1
180-
170-
160-
150-
Soil 1
Variety 1
π
Soil 2
0
Normal Q-Q Plot
(Left): All residuals plotted with diagonal line.
000000000000000
•
Theoretical Quantiles
●
Soil 3
000000000
1
-10
Soil 1
O
2
Variety 2
• D
Soil 2
Soil
•
model2$residuals
Soil 3
10
•+•
-10-
Soil 1
Variety 3
(Right): Residuals (y-axis) plotted against
predicted values (x-axis)
155
•
Soil 2
Soil 3
160
165
model2$fitted.values
170
175
Transcribed Image Text:Sample Quantiles 10 5 0 -5 -10 -15 O -2 yield -1 180- 170- 160- 150- Soil 1 Variety 1 π Soil 2 0 Normal Q-Q Plot (Left): All residuals plotted with diagonal line. 000000000000000 • Theoretical Quantiles ● Soil 3 000000000 1 -10 Soil 1 O 2 Variety 2 • D Soil 2 Soil • model2$residuals Soil 3 10 •+• -10- Soil 1 Variety 3 (Right): Residuals (y-axis) plotted against predicted values (x-axis) 155 • Soil 2 Soil 3 160 165 model2$fitted.values 170 175
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