solution

Suppose an experiment employing a randomized block design has four treatments and nine blocks, for a total of 4 Â 9 = 36 observations. Assume that the Total Sum of Squares for the response is SS1Total2 = 500. For each of the following partitions of SS(Total), test the null hypothesis that the treatment means are equal and test the null hypothesis that the block means are equal. Use Â = .05 for each test.

a. The Sum of Squares for Treatments (SST) is 20% of SS(Total), and the Sum of Squares for Blocks (SSB) is 30% of SS(Total).

b. SST is 50% of SS(Total), and SSB is 20% of SS(Total).

Â c. SST is 20% of SS(Total), and SSB is 50% of SS(Total).

d. SST is 40% of SS(Total), and SSB is 40% of SS(Total).

e. SST is 20% of SS(Total), and SSB is 20% of SS(Total).

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