1. Twelve orange pulp silage samples were divided at random into four
groups of three. One group was left as an untreated control while
the other three groups were treated with formic acid, beet pulp, and
sodium chloride, respectively. The observed moisture content of the
silage samples are shown below.
Sodium chloride Formic acid Beet pulp Control
80.5 89.1 77.8 76.7
79.3 75.7 79.5 77.2
79.0 81.2 77.0 78.6
(a) Obtain an analysis of variance table for the data and test the null
hypothesis that all four treatments yield the same true average
moisture content. Use α = 0.05.
(b) Compute a 99% confidence interval for the difference in response
between the average of the three treatment groups (acid, pulp,
and salt) and the control group.
(c) Compute 95% simultaneous confidence intervals for the differences
in response between each of the three treatment groups versus the
control group. Use the method among Bonferroni, Tukey, and
Scheff´e, that give the shortest intervals.
2. In an experiment with five treatment groups and 25 residual degrees of
freedom, for what numbers of contrasts is the Bonferroni method more
powerful than the Scheff´e method?
