A researcher wants to determine the impact of soil type on the growth of a certa

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.

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?

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

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

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

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

Explanation / Answer

One-way ANOVA: Height versus Soil Type

Source DF SS MS F P
Soil Type 3 19.670 6.557 7.01 0.013
Error 8 7.487 0.936
Total 11 27.157

S = 0.9674 R-Sq = 72.43% R-Sq(adj) = 62.09%

Ans:

b) The SS of treatment is 19.670.

c) The DF of error is 8.

d) The value of F statistic is 7.010.

e) Conclusion: The ertimated p-value is 0.013 and less than 0.10 level of significance. Hence, we can conclude that their is significantly different mean heights of plant at differnt types of soil. (The mean growth of the plant is not the same for all soil types).

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