Question
In: Statistics and Probability
Consider the experimental results for the following randomized block design. Make the calculations necessary to set...
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 | 15 | 14 | |
| 4 | 20 | 18 | 18 | |
| 5 | 8 | 7 | 9 | |
Use α = 0.05 to test for any significant differences.
State the null and alternative hypotheses.
H0: μA ≠
μB ≠ μC
Ha: μA =
μB = μC
H0: At least two of the population means are
equal.
Ha: At least two of the population means are
different.
H0: μA =
μB = μC
Ha: μA ≠
μB ≠ μC
H0: μA =
μB = μC
Ha: Not all the population means are equal.
H0: Not all the population means are
equal.
Ha: μA =
μB = μC
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 H0. There is sufficient evidence to conclude that the means of the three treatments are not equal.
Reject H0. There is not sufficient evidence to conclude that the means of the three treatments are not equal.
Do not reject H0. There is not sufficient evidence to conclude that the means of the three treatments are not equal.
Do not reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal.
Solutions
Expert Solution
Applying 2 way ANOVA":
from above:
H0: μA =
μB = μC
Ha: Not all the population means are equal.
value of the test statistic. =4.98
p-value =0.039
since p value <0.05
Reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal.
orchestra answered 1 year agoRelated Solutions
Consider the experimental results for the following randomized block design. Make the calculations necessary to set...
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
9
9
8
2
12
6
5
3
18
15
14
4
20
18
18
5
8
7
8
Use α = 0.05 to test for any significant
differences.
Find the value of the test statistic. (Round your answer to two
decimal places.)___
Find the p-value. (Round your answer to three decimal...
Consider the experimental results for the following randomized block design. Make the calculations necessary to set...
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
10
8
2
12
6
5
3
18
15
14
4
20
18
18
5
8
7
8
Use α = 0.05 to test for any significant
differences.
Find the value of the test statistic. (Round your answer to two
decimal places.)
Find the p-value. (Round your answer to three decimal...
Consider the experimental results for the following randomized block design. Make the calculations necessary to set...
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
7
8
Use α = 0.05 to test for any significant differences.
Find the value of the test statistic. (Round your answer to two
decimal places.)
__________.
Find the p-value. (Round your answer to three...
Consider the experimental results for the following randomized block design. Make the calculations necessary to set...
Consider the experimental results for the following randomized
block design. Make the calculations necessary to set up the
analysis of variance table.
Treatment
A
B
C
1
11
10
8
2
12
6
6
Blocks
3
18
16
15
4
20
18
18
5
9
7
9
Use a=.05 to test for any significant differences. Show entries
to 2 decimals, if necessary. Round all intermediate values to two
decimal places in your calculations. If your answer is zero enter
"0"....
Consider the experimental results for the following randomized block design. Tasks A B C Individuals 1...
Consider the experimental results for the following randomized
block design.
Tasks
A
B
C
Individuals
1
10
9
8
2
12
6
5
3
18
15
14
4
20
18
18
5
8
7
8
Suppose that you have an experiment wherein 5 individuals are
each receiving training on 3 different tasks (A, B, and C). The
values represent the number of minutes taken to complete the task.
Suppose further that we are interested in determining whether there
is a...
The following data are from a completely randomized design. In the following calculations, use α =...
The following data are from a completely randomized design. In
the following calculations, use α = 0.05 (level of
significance)
Treatment 1
Treatment 2
Treatment 3
63
82
69
47
72
54
54
88
61
40
66
48
sample mean
51
77
58
sample variance
96.67
97.34
81.99
a. Use analysis of variance to test for a significant difference
among the means of the three treatments.
b. Use Fisher’s LSD procedure to determine which means are
different.
The following data are from a completely randomized design. In the following calculations, use α =...
The following data are from a completely randomized design. In
the following calculations, use
α = 0.05.
Treatment
1
Treatment
2
Treatment
3
64
81
68
48
71
55
53
88
60
43
64
49
xj
52
76
58
sj2
80.67
112.67
64.67
(a)Use analysis of variance to test for a significant difference
among the means of the three treatments.
State the null and alternative hypotheses.
H0: At least two of the population means are
equal.
Ha: At least two...
The following data are from a completely randomized design. In the following calculations, use α =...
The following data are from a completely randomized design. In
the following calculations, use
α = 0.05.
Treatment
1
Treatment
2
Treatment
3
62
83
68
46
71
55
53
88
62
39
70
47
xj
50
78
58
sj2
96.67
79.33
82.00
(a)
Use analysis of variance to test for a significant difference
among the means of the three treatments.
State the null and alternative hypotheses.
H0: At least two of the population means are
equal.
Ha: At least...
The following data are from a completely randomized design. In the following calculations, use α =...
The following data are from a completely randomized design. In
the following calculations, use
α = 0.05.
Treatment
1
Treatment
2
Treatment
3
64
82
69
48
73
53
55
89
61
37
68
45
xj
51
78
57
sj2
130.00
87.33
106.67
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 = ____
+Use Fisher's LSD procedure to determine which means are
different....
The following data are from a completely randomized design. In the following calculations, use α =...
The following data are from a completely randomized design. In
the following calculations, use
α = 0.05.
Treatment
1
Treatment
2
Treatment
3
63
82
69
46
72
54
53
87
62
46
63
47
xj
52
76
58
sj2
64.67
114.00
91.33
(a)
Use analysis of variance to test for a significant difference
among the means of the three treatments.
State the null and alternative hypotheses.
H0: μ1 =
μ2 = μ3
Ha: Not all the population means are...
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