Question
In: Statistics and Probability
Develop the analysis of variance computations for the following completely randomized design. At α = 0.05,...
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 | 108 | 92 | |
| 119 | 115 | 81 | |
| 112 | 124 | 85 | |
| 107 | 103 | 102 | |
| 131 | 107 | 88 | |
| 113 | 108 | 118 | |
| 129 | 96 | 111 | |
| 113 | 115 | 120 | |
| 103 | 97 | ||
| 81 | 106 | ||
|
xj |
120 | 106 | 100 |
|
sj2 |
112.86 | 137.56 | 187.56 |
State the null and alternative hypotheses.
H0: μA =
μB = μC
Ha: μA ≠
μB ≠
μCH0:
μA ≠ μB ≠
μC
Ha: μA =
μB =
μC H0:
μA = μB =
μC
Ha: Not all the population means are
equal.H0: At least two of the population means
are equal.
Ha: At least two of the population means are
different.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 four decimal places.)
p-value =
State your conclusion.
Do not reject H0. There is 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. Reject H0. There is not sufficient evidence to conclude that the means of the three treatments are not equal.Reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal.
Solutions
Expert Solution
(a)
Correct option:
H0: 
Ha: 
(b)
From the given data, the following Table is constructed.
| Treatment A | Treatment B | Treatment C | Total | |
| N | 8 | 10 | 10 | 28 |
 |
960 | 1060 | 1000 | 3020 |
| Mean | 960/8=120 | 1060/10=106 | 1000/10=100 | 3020/28=107.857 |
 |
115990 | 113598 | 101688 | 331276 |
| Std. Dev. | 10.6234 | 11.7284 | 13.6951 | 14.3339 |
From the above Table, ANOVA Table is calculated as follows:
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Sum of Squares | F |
| Between treatments | 1831.4286 | 2 | 1831.4286/2=915.7143 | 915.7143/148.64=6.1606 |
| Within treatments | 3716 | 25 | 3716/25=148.64 | |
| Total | 5547.4286 | 27 |
Test Statistic is given by:
F = 915.7143/148.64= 6.16
(c)
Degrees of freedom for numerator = 2
Degrees of freedom for denominator = 25
By Technology, P - Value = 0.0067
(d)
Correct option:
Reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal.
orchestra answered 1 year agoRelated Solutions
Develop the analysis of variance computations for the following completely randomized design. At α = 0.05,...
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
135
106
93
120
114
82
114
124
84
106
104
102
132
107
90
115
108
117
128
96
110
102
115
120
104
99
82
93
xj
119
106
99
sj2
143.71
128.67
173.56
State the null and alternative hypotheses.
H0: Not all the population means are
equal.
Ha:...
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?
You may need to use the appropriate technology to answer this
question.
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
137
106
92
120
115
83
113
124
84
106
104
102
130
108
89
114
110
117
130
97
111
102
113
119
105
98
88
105
xj
119
107
100
sj2
155.14
97.11
170.44
State the null...
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...
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
82
69
46
73
53
53
89
61
39
60
45
xj
50
76
57
sj2
96.67
156.67
106.67
(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: μ1 ≠
μ2 ≠ μ3
Ha: μ1 =
μ2 = μ3
H0:...
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
73
53
53
89
60
43
69
55
xj
52
78
59
sj2
80.67
78.67
44.67
(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: μ1 ≠
μ2 ≠ μ3
Ha: μ1 =
μ2 = μ3
H0:...
The following data are from a completely randomized design.
You may need to use the appropriate technology to answer this
question.
The following data are from a completely randomized design.
Treatment
A
B
C
162
142
126
142
157
123
166
123
138
144
142
140
148
137
150
168
157
127
Sample
mean
155
143
134
Sample
variance
135.6
166.0
108.4
(a)
Compute the sum of squares between treatments.
(b)
Compute the mean square between treatments.
(c)
Compute the sum of squares due to error.
(d)
Compute the...
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