Question

Tomato weights and Fertilizer (Raw Data, Software Required):
Carl the farmer has three fields of tomatoes, on one he used no fertilizer, in another he used organic fertilizer, and the third he used a chemical fertilizer. He wants to see if there is a difference in the mean weights of tomatoes from the different fields. The sample data for tomato-weights in grams is given below. Carl claims there is a difference in the mean weight for all tomatoes between the different fertilizing methods.

No Fertilizer	Organic Fertilizer	Chemical Fertilizer
123	112	115
119	127	141
95	138	143
97	133	134
94	140	129
120	114	134
114	126	135
118	134	129
129	123	113
128	146	149

The Test: Complete the steps in testing the claim that there is a difference in the mean weight for all tomatoes between the different fertilizing methods.

(a) What is the null hypothesis for this test?

H₀: At least one of the population means is different from the others.H₀:  μ₁ ≠ μ₂ ≠ μ₃.    H₀:  μ₁ = μ₂ = μ₃.H₀:  μ₃ > μ₂ > μ₁.

(b) What is the alternate hypothesis for this test?

H₁: At least one of the population means is different from the others.H₁:  μ₁ ≠ μ₂ ≠ μ₃.    H₁:  μ₁ = μ₂ = μ₃.H₁:  μ₃ > μ₂ > μ₁.

(c) Use software to get the P-value of the test statistic ( F ). Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis at the 0.10 significance level?

reject H₀fail to reject H₀    

(e) Choose the appropriate concluding statement.

We have proven that all of the mean weights are the same.There is sufficient evidence to conclude that the mean weights are different.    There is not enough evidence to conclude that the mean weights are different.

(f) Does your conclusion change at the 0.01 significance level?

YesNo    

Answer 1

(a) What is the null hypothesis for this test?

Ans:   H₀:  μ₁ = μ₂ = μ₃

(b) What is the alternative hypothesis for this test?

Ans:

H₁: At least one of the population means is different from the others.

(c) Use software to get the P-value of the test statistic ( F ). Round to 4 decimal places unless your software automatically rounds to 3 decimal places.

Ans:

One-way ANOVA: Tomato versus methods

Source	DF	SS	MS	F	P
methods	2	1980	990	6.8750	0.0039
Error	27	3898	144
Total	29	5878

S = 12.02 R-Sq = 33.69% R-Sq(adj) = 28.77%

P-value =0.0039

(d) What is the conclusion regarding the null hypothesis at the 0.10 significance level?

Ans: reject H₀

(e) Choose the appropriate concluding statement.

Ans: There is sufficient evidence to conclude that the mean weights are different.

(f) Does your conclusion change at the 0.01 significance level?

Ans: No,  our conclusion do not change at the 0.01 significance level.