Suppose an experiment utilizing a random block design has 4 treatments and 10 blocks for a total of 40 observations. Assume that the total Sum of Squares for the response is SS(Total) = 300. If the Sum of Squares for Treatments (SST) is 20% of SS(Total), and the Sum of Squares for Blocks (SSB) is 40% of SS (Total), find the F values for this experiment.
A) treatments: F = 4.50; blocks: F = 3.00
B) treatments: F = 3.38; blocks: F = 2.70
C) treatments: F = 6.5; blocks: F = 4.33
D) treatments: F = 20.83; blocks: F = 6.94

Question

Quizplus · Accepted Answer

SST = 20% of SS(Total) = 0.20 * 300 = 60SSB = 40% of SS (Total) = 0.40 * 300 = 120SSE = SS(Total) - SST - SSB = 300 - 60 - 120 = 120dfT = 4 - 1 = 3dfB = 10 - 1 = 9dfE = 40 - 4 - 10 + 1 = 26MST = SST / dfT = 60 / 3 = 20MSB = SSB / dfB = 120 / 9 = 13.33MSE = SSE / dfE = 120 / 26 = 4.62F treatments = MST / MSE = 20 / 4.62 = 4.33F blocks = MSB / MSE = 13.33 / 4.62 = 2.88

Suppose an Experiment Utilizing a Random Block Design Has 4