This question wasn\'t answered so posting again. A researcher wants to determine

ID: 3225911 • Letter: T

Question

This question wasn't answered so posting again.

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.

a) What null hypothesis is the researcher testing if she runs an ANOVA with this data? Possible answers:

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

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

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

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

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

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

c) What is DFerr 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 0.1 level of significance, what conclusion should the researcher reach?

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

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

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

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

Row Soil 1 Soil 2 Soil 3 Soil 4 1 11.4 12.5 10.2 12 2 11.2 12.3 9.4 11 3 11.9 12.6 8.3 14.2

Explanation / Answer

Part-a

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

Part-b

Results of anova are as follows from where SStrt=19.67

Anova: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

Soil 1

34.5

11.5

0.13

Soil 2

37.4

12.46666667

0.023333333

Soil 3

27.9

9.3

0.91

Soil 4

37.2

12.4

2.68

ANOVA

Source of Variation

P-value

F crit

Between Groups

19.67

6.556666667

7.006233304

0.012544903

2.923796288

Within Groups

7.486666667

0.935833333

Total

27.15666667

Part-c

The DFerr for the ANOVA=8

Part-d

The value of the F statistic for the ANOVA=7.006

Part-e