Answer:
(1) Option a
(2) 13.737
(3) 8
(4) 3.803
(5) Option a
Step-by-step explanation:
In this case, we need to determine whether the soil type effects the growth of a certain type of plant.
Perform the ANOVA test for the provided data on Excel.
Go to Data - Data Analysis - Anova: Single factor
Select the data for the growth.
Press OK.
The output is attached below.
(1)
The hypothesis for the study can be defined as follows:
H₀: The mean growth of the plant in each type of soil is the same.
Hₐ: The mean growth of the plant is different in each type of soil.
Correct option a.
(2)
The sum of square for treatment is:
[tex]\text{SS}_{trt}=\text{SS}_{BG}=13.737[/tex]
(3)
The degrees of freedom of error is:
[tex]\text{DF}_{err}=\text{DF}_{WG}=8[/tex]
(4)
The F statistic for the ANOVA is:
[tex]F=3.803[/tex]
(5)
The p-value of the test is:
[tex]p-value=0.058[/tex]
Decision Rule:
Reject H₀ if the p-value of the test is less than the level of significance.
[tex]\text{p-value}=0.058>\alpha=0.05[/tex]
The null hypothesis was failed to be rejected.
Conclusion:
There is not enough evidence to reject the claim that the mean growth of the plant is the same in each type of soil.
Correct option a.
