Solution Found!
Suppose an experiment employing a randomized block design
Chapter 9, Problem 53E(choose chapter or problem)
Suppose an experiment employing a randomized block design has four treatments and nine blocks, for a total of \(4\ \times\ 9\ =\ 36\) observations. Assume that the Total Sum of Squares for the response is SS(Total) = 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 \(\alpha\ =\ .05\) 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).
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).
Questions & Answers
QUESTION:
Suppose an experiment employing a randomized block design has four treatments and nine blocks, for a total of \(4\ \times\ 9\ =\ 36\) observations. Assume that the Total Sum of Squares for the response is SS(Total) = 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 \(\alpha\ =\ .05\) 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).
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).
ANSWER:Step 1 of 29
It is given that a randomized block design has four treatments and 9 blocks, for a total of 4 x 9 = 36 observations.
Total Sum of Squares, SS(Total) = 500