2. Consider an experiment to compare 7 treatments in blocks of size 5, with an anticipated...

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2. Consider an experiment to compare 7 treatments in blocks of size 5, with an anticipated error variance of at most 30 squared units. (a) [2pts] Verify that the following conditions cannot be satisfied with less than b = 21 blocks vr = bk r(k − 1) = X(v - 1) [Hint: For each b ≤ 20, calculate r and A according to the above formula. Show the b = 21 is the minimum that yields both an integer r and an integer X. ] (b) [3pts] Assuming that a balanced incomplete block design exists with b = 10 blocks and r = 6, and the error variance is at most 30 squared units, calculate the width of 95% simultaneous confidence intervals of a pairwise comparison using Tukey's method. (c) [3pts]Repeat part (b) using Dunnett's method for treatment versus control comparisons. 2. Consider an experiment to compare 7 treatments in blocks of size 5, with an anticipated error variance of at most 30 squared units. (a) [2pts] Verify that the following conditions cannot be satisfied with less than b = 21 blocks vr = bk r(k − 1) = X(v - 1) [Hint: For each b ≤ 20, calculate r and A according to the above formula. Show the b = 21 is the minimum that yields both an integer r and an integer X. ] (b) [3pts] Assuming that a balanced incomplete block design exists with b = 10 blocks and r = 6, and the error variance is at most 30 squared units, calculate the width of 95% simultaneous confidence intervals of a pairwise comparison using Tukey's method. (c) [3pts]Repeat part (b) using Dunnett's method for treatment versus control comparisons.

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a The condition er bk cannot be satisfied with less than 21 blocks This is because r and k must be i... View the full answer