Question

The following data were obtained for a randomized block design
involving five treatments and three blocks: SST = 510, SSTR = 370,
SSBL = 95. Set up the ANOVA table. (Round your value for *F*
to two decimal places, and your *p*-value to three decimal
places.)

Source of Variation |
Sum of Squares |
Degrees of Freedom |
Mean Square |
F |
p-value |
---|---|---|---|---|---|

Treatments | |||||

Blocks | |||||

Error | |||||

Total |

Test for any significant differences. Use *α* = 0.05.

State the null and alternative hypotheses.

*H*_{0}: Not all the population means are
equal.

*H*_{a}: *μ*_{1} =
*μ*_{2} = *μ*_{3} =
*μ*_{4} =
*μ*_{5}*H*_{0}:
*μ*_{1} = *μ*_{2} =
*μ*_{3} = *μ*_{4} =
*μ*_{5}

*H*_{a}: *μ*_{1} ≠
*μ*_{2} ≠ *μ*_{3} ≠
*μ*_{4} ≠
*μ*_{5} *H*_{0}:
At least two of the population means are equal.

*H*_{a}: At least two of the population means are
different.*H*_{0}: *μ*_{1} ≠
*μ*_{2} ≠ *μ*_{3} ≠
*μ*_{4} ≠ *μ*_{5}

*H*_{a}: *μ*_{1} =
*μ*_{2} = *μ*_{3} =
*μ*_{4} =
*μ*_{5}*H*_{0}:
*μ*_{1} = *μ*_{2} =
*μ*_{3} = *μ*_{4} =
*μ*_{5}

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

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.

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

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

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

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

Answer #1

Solution;-

Source of Variation |
Sum of squares |
Degree of Freedom |
Mean Square |
F | p-value |

Treatments | 370 | 4 | 92.5 | 16.444 | 0.001 |

Blocks | 95 | 2 | 47.5 | 8.4444 | 0.011 |

Error | 45 | 8 | 5.625 | ||

Total | 510 | 14 |

**State the hypotheses.** The first step is to
state the null hypothesis and an alternative hypothesis.

*H*_{a}: *μ*_{1} =
*μ*_{2} = *μ*_{3} =
*μ*_{4} = *μ*_{5}

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

**Formulate an analysis plan**. For this analysis,
the significance level is 0.05.

**Analyze sample data**.

F statistics is given by:-

**F = 16.444**

**The P-value = 0.001**

**Interpret results. Since the P-value (0.001) is less
than the significance level (0.05), we have to reject the null
hypothesis.**

**Conclusion:-**

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

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your values for mean squares and F to two decimal places,
and your p-value to three decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Treatments
900
Blocks
200
Error
Total
1,600
Use α = 0.05 to test for any significant
differences.
State the null and alternative hypotheses.
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nT = 19.
Set up the ANOVA table. (Round your values for MSE and
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decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
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F
p-value
Treatments
Error
Total
Test for any significant difference between the mean output
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units assembled correctly was recorded, and the analysis of
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Three different methods for assembling a product were proposed
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A
B
C
Blocks
1
10
9
8
2
12
6
5
3
18
16
14
4
20
18
18
5
8
7
8
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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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H0: μA =...

You may need to use the appropriate technology to answer this
question.
An experiment has been conducted for four treatments with seven
blocks. Complete the following analysis of variance table. (Round
your values for mean squares and F to two decimal places,
and your p-value to three decimal places.)
Source
of Variation
Sum
of Squares
Degrees
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Mean
Square
F
p-value
Treatments
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Blocks
700
Error
100
Total
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Use α = 0.05 to test for any significant
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You may need to use the appropriate technology to answer this
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A
B
C
136
108
91
119
115
81
113
125
85
106
105
102
130
108
88
115
109
117
129
96
109
112
115
121
104
99
85
107
xj
120
107
100
sj2
110.29
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25.2
25.3
27.1
20.5
31.3
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24.0
26.2
20.2
23.8
34.0
17.1
26.8
23.7
24.6
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30.1
34.0
27.5
29.4
28.0
26.2
29.9
29.5
30.0
35.6
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36.3
44.2
34.1
30.3
32.1
33.1
34.1
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88
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74
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