Question

Tomato weights and Fertilizer: 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 is given below. The second table gives the results from an ANOVA test. Carl claims there is a difference in the mean weight for all tomatoes between the different fertilizing methods.

Tomato-Weight in Grams

											x
No Fertilizer	123	119	95	97	94	120	114	118	129	128	113.7
Organic Fertilizer	112	127	138	133	140	114	126	134	123	144	129.1
Chemical Fertilizer	115	141	143	134	129	134	135	129	113	148	132.1

ANOVA Results

F	P-value
6.921	0.0037

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

(c) What is the conclusion regarding the null hypothesis at the 0.05 significance level?

reject H₀ fail to reject H₀    

(d) 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.

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

Yes No    

Answer 1

Tomato weights and Fertilizer: 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 is given below. The second table gives the results from an ANOVA test. Carl claims there is a difference in the mean weight for all tomatoes between the different fertilizing methods.

Tomato-Weight in Grams

											x
No Fertilizer	123	119	95	97	94	120	114	118	129	128	113.7
Organic Fertilizer	112	127	138	133	140	114	126	134	123	144	129.1
Chemical Fertilizer	115	141	143	134	129	134	135	129	113	148	132.1

ANOVA Results

F	P-value
6.921	0.0037

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: μ₁ = μ₂ = μ₃.

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

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

(c) What is the conclusion regarding the null hypothesis at the 0.05 significance level?

reject H₀

( obtained p value 0.0037 is less than 0.05 level of significance)

(d) Choose the appropriate concluding statement.

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

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

Yes

( obtained p value 0.0037 is less than 0.01 level of significance)

Excel used

One factor ANOVA
	Mean	n	Std. Dev
	113.7	10	13.45	No Fertilizer
	129.1	10	10.70	Organic Fertilizer
	132.1	10	11.27	Chemical Fertilizer
	125.0	30	14.08	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	1,949.07	2	974.533	6.921	.0037
Error	3,801.90	27	140.811
Total	5,750.97	29