Q1

Statistics

You may need to use the appropriate technology to answer this question. The following data are from a completely randomized design. Treatment C 161 142 127 143 156 122 164 124 138 145 141 140 149 135 151 174 148 132 Sample 156 141 135 mean Sample variance 150.4 120.0 106.4 (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 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 p-value Treatments Error Total(f) At the = 0.05 level of significance, test whether the means for the three treatments are equal. State the null and alternative hypotheses. O Hyi b = Hg = #e Hat Mp # Mg # M O HU: Not all the population means are equal. Hat Mp = g = He O Hg: At least two of the population means are equal. Ha: At least two of the population means are different. O Hy: pp = g = Ug Ha: Not all the population means are equal. O Hg: pp # Hg * He Hat Mp = g = 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. O De not reject Hg. There is sufficient evidence to conclude that the means for the three treatments are not equal. O Reject Hy. There is nat sufficient evidence to conclude that the means for the three treatments are not equal. O Reject HD' There is sufficient evidence to conclude that the means for the three treatments are not equal. O Do not reject HD. There is not sufficient evidence to conclude that the means for the three treatments are not equal