The variance ๐2 of an individual observation can be estimated in a number of
ways, depending on the situation. How many degrees of freedom are associated with the estimate s2 (of ๐2) in each of the following circumstances?
(a) A randomized paired comparison of two treatments A and B, where there
are nA = 22 observations with A and nB = 22 observations with B.
(b) A randomized unpaired comparison of two treatments A and B, where
there are nA = 21 observations with A and nB = 14 observations with B.
(c) An 8 ร 8 Latin square design.
(d) A 9 ร 9 Graeco-Latin square design.
(e) A one-way layout (factors with fixed levels) with five treatments, where
nA = 24, nB = 15, nC = 12, nD = 20, and nE = 17.
(f) A randomized block design with 6 blocks and 14 treatments.
(g) An experiment on 24 mice to compare four diet types A, B, C, and D,
with nA = 6, nB = 8, nC = 5, and nD = 5. The initial body weight of each
mouse is recorded as the covariate value. Analysis of covariance is used
to compare the effects of the four diet types.
(h) To study the strength of plastic, an experimenter prepares 16 batches
of plastic with two for each of the eight treatment combinations for: A,
temperature with 2 levels; and B, additive percentage with 4 levels. Four
batches with different additive percentages are baked for each temperature setting. A split-plot design and analysis are used to study the effects
of A and B.
(i) To increase the edible meat of cows, a pharmaceutical company developed a growth hormone to be fed to cattle. An experiment was set up to
study the effectiveness of the hormone produced from different batches,
among different herds of cattle. Five herds of cattle and four batches of
hormone-enhanced feed were randomly selected. From each herd and
hormone combination, the weights of the first 50 cows to be reared were
recorded.