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Develop the analysis of variance computations for the following completely randomized design. At α = 0.05, is there a significant difference between the treatment means?
Treatment | |||
---|---|---|---|
A | B | C | |
136 | 106 | 93 | |
119 | 113 | 83 | |
113 | 126 | 84 | |
106 | 103 | 101 | |
132 | 107 | 90 | |
114 | 109 | 116 | |
129 | 98 | 111 | |
103 | 115 | 119 | |
105 | 97 | ||
78 | 116 | ||
x_{j} |
119 | 106 | 101 |
s_{j}^{2} |
149.14 | 155.33 | 187.56 |
State the null and alternative hypotheses.
tH_{0}: At least two of the population means
are equal.
H_{a}: At least two of the population means are
different.
H_{0}: μ_{A} = μ_{B} =
μ_{C}
H_{a}: μ_{A} ≠ μ_{B} ≠
μ_{C}
H_{0}: Not all the population means are
equal.
H_{a}: μ_{A} = μ_{B} =
μ_{C}
H_{0}: μ_{A} = μ_{B} =
μ_{C}
H_{a}: Not all the population means are equal
H_{0}: μ_{A} ≠ μ_{B} ≠
μ_{C}
H_{a}: μ_{A} = μ_{B} =
μ_{C}
_{t}est statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Reject H_{0}. There is sufficient evidence to conclude that the means of the three treatments are not equal
.Do not reject H_{0}. There is sufficient evidence to conclude that the means of the three treatments are not equal.
Reject H_{0}. There is not sufficient evidence to conclude that the means of the three treatments are not equal
.Do not reject H_{0}. There is not sufficient evidence to conclude that the means of the three treatments are not equal.
The statistical software output for this problem is :
Option D is correct.
Test statistics = 4.53
P-value = 0.0209
Option A is correct .
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