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In: Statistics and Probability

Tomato weights and Fertilizer (Raw Data, Software Required): Carl the farmer has three fields of tomatoes,...

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
118 138 143
120 133 134
117 140 129
120 114 134
114 126 135
118 134 129
129 123 113
126 145 147

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


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

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


(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 0.01 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 0.10 significance level?

YesNo    

Solutions

Expert Solution

The statistical software output for this problem is :

H0:  μ1 = μ2 = μ3.  

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

P-value = 0.0257

fail to reject H0    

There is not enough evidence to conclude that the mean weights are different.

Yes

orchestra answered 1 year ago
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