Tomato weights and Fertilizer (Raw Data, Software Required): Carl the farmer has
ID: 3229335 • Letter: T
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.
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: 1 = 2 = 3.
H0: At least one of the population means is different from the others.
H0: 3 > 2 > 1.
(b) What is the alternate hypothesis for this test?
H1: At least one of the population means is different from the others.
H1: 1 2 3.
H1: 3 > 2 > 1.
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 0.01 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 0.10 significance level?
Yes
No
No Fertilizer Organic Fertilizer Chemical Fertilizer 123 112 115 119 127 141 95 138 143 97 133 134 94 140 129 120 114 134 114 126 135 118 134 129 129 123 113 126 143 150Explanation / Answer
from above
a) H0: 1 = 2 = 3.
b)H1: At least one of the population means is different from the others
c) P vlaue =0.0031
d)reject H0
e)There is sufficient evidence to conclude that the mean weights are different
f)No
SUMMARY Groups Count Sum Average Variance No Fertilizer 10 1135 113.5 174.9444 Organic Fertilizer 10 1290 129 111.3333 Chemical Fertilizer 10 1323 132.3 134.4556 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 2015.267 2 1007.633 7.184836 0.003149 3.354131 Within Groups 3786.6 27 140.2444 Total 5801.867 29