Answer to Question #241047 in Statistics and Probability for Mary Jean

Question

In a bioligical experiment 4 concentration of a certain chemical are used to enhance the growth of a certain type of plant over specified period of time.the following growth data,in centimeters,were recorded for the plant that survived: Concentration column 1 is 8.2 ,8.7 ,9.4, 9.2 column 2 is 7.7, 8.4,8.6,8.1,8.0 column 3 is 6.9 , 5.8 ,7.2,6.8,7.4,6.1 and column 4 is 6.8,7.3,6.3,6.9,7.1.Is there a significant difference in the average growth of these plants for the different concentration of the chemicals ?Use a 0.01 level of significance.

Answer 1

Hypotheses

Ho: μ₁ = μ₂ = μ₃ = μ₄

H1: At least one of the means is significantly different

α =0.01

Test statistic

We will use F-statistic

Rejection region

We reject H₀ if the computed p-value <0.01

Computation of F-statistic

By using excel, we obtain the output below.

Anova: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

Concentration 1

4

35.5

8.875

0.289167

Concentration 2

5

40.8

8.16

0.123

Concentration 3

6

40.2

6.7

0.392

Concentration 4

5

34.4

6.88

0.142

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

15.462

3

5.154

21.2126

8.03E-06

5.2922

Within Groups

3.8875

16

0.2430

Total

19.3495

19

 

From the analysis, the computed F_(3,16) = 5.2922, p = 0.0000<0.01. We reject the null hypothesis meaning that the data provides sufficient evidence to conclude that at least one of the means is significantly different from the other means at 0.01alpha level of significance. This may imply that there is a significant difference in the average growth of these plants for the different concentrations of the chemicals.