Question

Plant Food Case

A garden center wishes to determine if there are in fact differences in the effect of three different brands of plant food on the growth of sunflowers and the rank of their effectiveness in promoting growth. To do so, they selected 15 sunflower seedlings at random from the greenhouse and fed 5 of the seedlings with Plant Food A, 5 with Plant Food B, and 5 with Plant Food C. The weekly growth of each seedling was measured in inches and is summarized below.

Plant Food A	Plant Food B	Plant Food C
3.8	5.4	1.3
1.2	2.0	0.7
4.1	4.8	2.2
5.5	4.6	1.1
2.3	3.7	1.4

1. Describe the purpose of the study
2. Conduct a Single Factor Analysis of Variance Hypothesis Test at alpha =.05
3. Explain the method used to set up and conduct the test
4. Describe the results
5. State a conclusion
6. Justify the conclusion

Answer 1

Here we have data:

Plant Food A	Plant Food B	Plant Food C
3.8	5.4	1.3
1.2	2	0.7
4.1	4.8	2.2
5.5	4.6	1.1
2.3	3.7	1.4

a) He we are trying to see that the there is any different in average growth of the sunflowers in all three food category.

b) Here we are using excel for calculation:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	5	16.9	3.38	2.777
Column 2	5	20.5	4.1	1.75
Column 3	5	6.7	1.34	0.303
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	20.496	2	10.248	6.3652	0.0131	3.8853
Within Groups	19.32	12	1.61
Total	39.816	14

c) Hypothesis:

H_o; μ₁ = μ₂ = μ₃

H_a; At least one mean is difference from others.

Test statistics :

F = 6.3652

P-value = 0.0131

Critical value :

F_c = 3.8853

e) Reject the null hypothesis

Here we have sufficient evidence to reject the null hypothesis, F-observed value is grater than F-crtical value and p-value is less than alpha value.

f ) We can say that in the all three food categories average growth of the sunflowers is not equal.