Question

16. Some completely randomized design has six (6) treatments with nine (9) observations collected from cach treatment. Assume all pairwise comparisons of treatment means are to be made using a multiple con- parisons procedure. Determine the total number of treatment means to be compared. (a) 36 (b) 15 (c) 27 (d) 105 17. An experiment was conducted using a completely randomized block design with eight (8) treatments and five (5) blocks. Find the degrees of freedom associated with MIST and the degrees of freedom associated with MISE. (a) 7 and 4 (b) 4 and 28 (c) 8 and 40 (d) 7 and 28 18. For some two-factor factorial experiment, factors A and B are respec- tively run at 3 and 7 levels. There are 2 replications for each factor-level combinations. We are asked to test for equality of treatment means. Find the rejection region for this test based on the 0.05 level. (a) F > 2.10 (b) F> 1.78 (c) F > 2.42 (d) F > 3.47

Answer 1

(16) (b): 15

>> Number of treatments = 6

For all pairwise comparison of treatment means, the total number of treatment means to be compared = 6C2 = 6!/(4!2!) = 15

(17) (d): 7 and 28

>> Degrees of freedom associated with MST = (8-1) = 7

Degrees of freedom associated with MSE = (8-1)(5-1) = 28

(18) (d): F > 3.47

>> Degrees of freedom associated with MSA = (3-1) = 2

Degrees of freedom associated with MSE = 3×7×(2-1) = 21

Critical value, F(0.05,2,21) = 3.4668 ≈ 3.47

The rejection region: F > 3.47