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

129 144 147

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:_{1 2 3}.

H₀:₃ > ₂ > ₁.

H₀:At least one of the population means is different from the others.

H₀:₁ = ₂ = ₃.

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

H₁:₁ = ₂ = ₃.

H₁:₃ > ₂ > ₁.

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

H₁:_{1 2 3}.

(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 H₀

fail 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 0.05 significance level?

Yes

No