The following data are from a completely randomized design. Sample mean Sample variance Treatment A B C 161 2 141 166 144 143 125 156 125 123 138 142 141 135 148 170 151 132 151 155 142 135 149.6 123.2 110.8 (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 mean square due to error. (Round your answer to two decimal places.)

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The following data are from a completely randomized design.
Sample
mean
Sample
variance
A
161
141
166
144
148
170
155
Treatment
B
143
156
125
142
135
151
142
C
125
123
138
141
151
132
135
149.6 123.2 110.8
(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 mean square due to error. (Round your answer to two decimal places.)
Transcribed Image Text:The following data are from a completely randomized design. Sample mean Sample variance A 161 141 166 144 148 170 155 Treatment B 143 156 125 142 135 151 142 C 125 123 138 141 151 132 135 149.6 123.2 110.8 (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 mean square due to error. (Round your answer to two 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
Sum
Degrees
Mean
of Variation of Squares of Freedom Square
Treatments
Error
Total
Ho: Not all the population means are equal.
Ha: MA = MB = MC
(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.
Ho: MAMB MC
Ha MAMB = MC
Ho: MA = MB = MC
Ha: MAMB MC
#
Ho MA = MB = mc
Ha: Not all the population means are equal.
F
Ho:
At least two of the population means are equal.
H₂: 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 four decimal places.)
p-value =
p-value
State your conclusion.
Do not reject Ho. There is not sufficient evidence to conclude that the means for the three treatments are not equal.
Do not reject Ho.
There is sufficient evidence to conclude that the means for the three treatments are not equal.
Reject Ho. There is not sufficient evidence to conclude that the means for the three treatments are not equal.
Reject Ho. There is sufficient evidence to conclude that the means for the three treatments are not equal.
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 Sum Degrees Mean of Variation of Squares of Freedom Square Treatments Error Total Ho: Not all the population means are equal. Ha: MA = MB = MC (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. Ho: MAMB MC Ha MAMB = MC Ho: MA = MB = MC Ha: MAMB MC # Ho MA = MB = mc Ha: Not all the population means are equal. F Ho: At least two of the population means are equal. H₂: 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 four decimal places.) p-value = p-value State your conclusion. Do not reject Ho. There is not sufficient evidence to conclude that the means for the three treatments are not equal. Do not reject Ho. There is sufficient evidence to conclude that the means for the three treatments are not equal. Reject Ho. There is not sufficient evidence to conclude that the means for the three treatments are not equal. Reject Ho. There is sufficient evidence to conclude that the means for the three treatments are not equal.
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