Question

You may need to use the appropriate technology to answer this question.

Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table.

Treatments | ||||
---|---|---|---|---|

A | B | C | ||

Blocks | 1 | 10 | 9 | 8 |

2 | 12 | 7 | 5 | |

3 | 18 | 15 | 14 | |

4 | 20 | 18 | 18 | |

5 | 8 | 7 | 8 |

Use *α* = 0.05 to test for any significant
differences.

State the null and alternative hypotheses.

*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}: 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}: At least two of the population means are
equal.

*H*_{a}: At least two of the population means are
different.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the *p*-value. (Round your answer to three 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 not 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.

Answer #1

from excel": data -data analysis: ANOVA without replication

Source of Variation |
SS |
df |
MS |
F |
P-value |

block | 304.4 | 4 | 76.1 | 41.14 | 0.000 |

treatment | 25.2 | 2 | 12.6 | 6.81 | 0.019 |

Error | 14.8 | 8 | 1.85 | ||

Total | 344.4 | 14 |

*H*_{0}: μ_{A} = μ_{B} =
μ_{C}

*H*_{a}: Not all the population means are equal.

value of the test statistic =6.81

*p*-value =0.019

Reject *H*_{0}. There is sufficient evidence to
conclude that the means of the three treatments are not equal.

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83
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106
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105
97
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xj
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106
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sj2
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Consider the experimental results for the following randomized
block design. Make the calculations necessary to set up the
analysis of variance table.
Treatments
A
B
C
Blocks
1
10
9
8
2
12
6
5
3
18
16
14
4
20
18
18
5
8
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Use α = 0.05 to test for any significant
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State the null and alternative hypotheses.
H0: Not all the population means are
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Ha: μA =
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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
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136
108
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115
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125
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88
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109
117
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99
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