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.

Inches	Soil
11	1
12.3	1
11.4	1
13	2
9.5	2
11.9	2
10.1	3
8.2	3
7.9	3
12.8	4
12.5	4
12.5	4

a) 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. Soil 3 provides a lower mean growth for the plant than the other types of soil.  

c. The variability in growth of the plant in each type of soil is the same.

d. One type of soil has a higher mean growth for the plant than the others.

e. The mean growth of the plant is different in each type of soil.

.

b) What is the SS_trt for the ANOVA? Give your answer to at least three decimal places.

.

c) What is DF_err for the ANOVA?

.

d) What is the value of the F statistic for the ANOVA? Give your answer to at least three decimal places.

.

e) Using a 0.05 level of significance, what conclusion should the researcher reach?

a. Soil 3 has a lower mean growth for the plant than the other types of soil.

b. There is not enough evidence to reject the claim that the mean growth of the plant is the same in each type of soil.

c. Soil 1 has a higher mean growth for the plant than the other types of soil.

d. The mean growth of the plant is not the same for all soil types.

Answer 1

applying one way ANOVA:

Source of Variation	SS	df	MS	F	P-value
Between Groups	24.6092	3	8.2031	6.4338	0.0159
Within Groups	10.2000	8	1.2750
Total	34.8092	11

a)

H0: μ1 = μ2 = μ3=μ4

H1: There is at least one mean difference among the populations.

a. The mean growth of the plant in each type of soil is the same

b) SS_tr =24.609

c) DF_err =8

d) value of the F statistic =6.434

e)

d. The mean growth of the plant is not the same for all soil types.