Question: The following data are from a completely randomized design. Treatment A B C 162 143 126 142 157 121 165 125 139 145 143 139

The following data are from a completely randomized design. Treatment A B C 162 143 126 142 157 121 165 125 139 145 143 139 148 136 150 174 154 123 Sample 156 143 133 mean Sample 164.4 138.0 130.8 variance (a) Compute the sum of squares between treatments. 1488 X (b) Compute the mean square between treatments. 744 X (c) Compute the sum of squares due to error. 2166 (d) Compute the mean square due to error. (Round your answer to two decimal places.) 144.4 (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 p-value of Variation of Squares of Freedom Square Treatments 1488 X X X 744 X X Error X X X Total X X (f) At the a = 0.05 level of significance, test whether the means for the three treatments are equal. State the null and alternative hypotheses. OHO: HA * HB # HC Ha: HA = HB = HC O Ho: Not all the population means are equal. Ha: HA = HB = HC O HO: HA = HB = HC Ha: HA * HB # HC O Ho: At least two of the population means are equal. Ha: At least two of the population means are different. HO: HA = MB = HC Ha: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) X Find the p-value. (Round your answer to four decimal places.) p-value = 0.0162 X 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. O Reject Ho. There is sufficient evidence to conclude that the means for the three treatments are not equal. O Reject Ho. There is not sufficient evidence to conclude that the means for the three treatments are not equal

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