Question

A researcher wants to determine the impact of soil type on the growth of a certain type of plant. She grows three plants in each of four different types of soil and measures the growth in inches for each plant after one month resulting in the data below.

Soil 1 Soil 2 Soil 3 Soil 4
12.6 12.2 12.2 11.1
12.6 12 10.6 11.7
14.3 13 9.1 9.6

1. What null hypothesis is the researcher testing if she runs an ANOVA with this data?

a.The mean growth of the plant in each type of soil is the same.
b. One type of soil has a higher mean growth for the plant than the others.
c. The variability in growth of the plant in each type of soil is the same.
d. Oil 3 provides a lower mean growth for the plant than the other types of soil.
e. The mean growth of the plant is different in each type of soil.

2. What is the SStrt for the ANOVA? Give your answer to at least three decimal places.
3. What is DFerr for the ANOVA?
4. What is the value of the F statistic for the ANOVA? Give your answer to at least three decimal places.
5. Using a 0.05 level of significance, what conclusion should the researcher reach?

a. There is not enough evidence to reject the claim that the mean growth of the plant is the same in each type of soil.
b. Soil 1 has a higher mean growth for the plant than the other types of soil.
c. The mean growth of the plant is not the same for all soil types .
d. Soil 3 has a lower mean growth for the plant than the other types of soil.

Answer 1

(1) Option a

(2) 13.737

(3) 8

(4) 3.803

(5) Option a

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:

`\text{SS}_(trt)=\text{SS}_(BG)=13.737`

(3)

The degrees of freedom of error is:

`\text{DF}_(err)=\text{DF}_(WG)=8`

(4)

The F statistic for the ANOVA is:

`F=3.803`

(5)

The p-value of the test is:

`p-value=0.058`

Decision Rule:

Reject H₀ if the p-value of the test is less than the level of significance.

`\text{p-value}=0.058>\alpha=0.05`

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.