(a) Compute the sum of squares between treatments. X (b) Compute the mean square between treatments. 0 (c) Compute the sum of squares due to error. (d) Compute the mean square due to error. (Round your answer to two decimal places.) X

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 8E
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The following data are from a completely randomized design.
Sample
mean
Sample
variance
0
A
162
141
166
144
148
175
156
Treatment
B
141
156
123
143
137
158
143
C
127
122
139
139
149
122
133
186.0 166.8 121.2
(a) Compute the sum of squares between treatments.
X
(b) Compute the mean square between treatments.
X
(c) Compute the sum of squares due to error.
X
(d) Compute the mean square due to error. (Round your answer to two decimal places.)
X
(e) Set up the ANOVA table for this problem. (Round your values for MSE and F to two decimal places, and your p-value
to four decimal places.)
Transcribed Image Text:You may need to use the appropriate technology to answer this question. The following data are from a completely randomized design. Sample mean Sample variance 0 A 162 141 166 144 148 175 156 Treatment B 141 156 123 143 137 158 143 C 127 122 139 139 149 122 133 186.0 166.8 121.2 (a) Compute the sum of squares between treatments. X (b) Compute the mean square between treatments. X (c) Compute the sum of squares due to error. X (d) Compute the mean square due to error. (Round your answer to two decimal places.) X (e) Set up the ANOVA table for this problem. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)
(e) Set up the ANOVA table for this problem. (Round your values for MSE and F to two decimal places, and your p-value
to four decimal places.)
Source
of Variation
Treatments
Error
Total
Sum
Degrees
of Squares of Freedom
Ho: MA= B = MC
Ha: MA MB MC
Ho: Not all the population means are equal.
Ha HA = MB = AC
(f) At the α = 0.05 level of significance, test whether the means for the three treatments are equal.
State the null and alternative hypotheses.
OHO: MAMB #Mc
H₂: MA= MB = MC
O Ho: At least two of the population means are equal.
H₂: At least two of the population means are different.
Mean
Square
O HOMA = MB = MC
H₂: 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 four decimal places.)
p-value =
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State your conclusion.
O Reject Ho. There is not sufficient evidence to conclude that the means for the three treatments are not equal.
O Reject Ho. There is sufficient evidence to conclude that the means for the three treatments are not equal.
O Do not reject Ho. There is not sufficient evidence to conclude that the means for the three treatments are not
equal.
F
O Do not reject Ho. There is sufficient evidence to conclude that the means for the three treatments are not
equal.
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Transcribed Image Text:(e) Set up the ANOVA table for this problem. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.) Source of Variation Treatments Error Total Sum Degrees of Squares of Freedom Ho: MA= B = MC Ha: MA MB MC Ho: Not all the population means are equal. Ha HA = MB = AC (f) At the α = 0.05 level of significance, test whether the means for the three treatments are equal. State the null and alternative hypotheses. OHO: MAMB #Mc H₂: MA= MB = MC O Ho: At least two of the population means are equal. H₂: At least two of the population means are different. Mean Square O HOMA = MB = MC H₂: 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 four decimal places.) p-value = Need Help? Submit Answer State your conclusion. O Reject Ho. There is not sufficient evidence to conclude that the means for the three treatments are not equal. O Reject Ho. There is sufficient evidence to conclude that the means for the three treatments are not equal. O Do not reject Ho. There is not sufficient evidence to conclude that the means for the three treatments are not equal. F O Do not reject Ho. There is sufficient evidence to conclude that the means for the three treatments are not equal. Read It Watch It p-value Viewing Saved Work Revert to Last Response
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