Bethea et al. (1985) reported data on an experiment to determine the effectiveness of four adhesive systems for bonding insulation to a chamber. The data are a measure of the peel-strength of the adhesives and are presented in Table 12.16. A disturbing aspect of these data is that the values for adhesive system 3 are reported with an extra digit.

(a) Compute the sample means and variances for each group. Give the one-way analysis of variance model with all of its assumptions. Are there problems with the assumptions? If so, does an analysis on the square roots or logs of the data reduce these problems?

(b) Give the analysis of variance table for these (possibly transformed) data. Test whether there are any differences in adhesive systems. Use α = 0.01.

Table 12.16: Peel-strength of various adhesive systems.
Adhesive system Observations 1 60 63 57 53 56 57 2 57 52 55 59 56 54 3 19.8 19.5 19.7 21.6 21.1 19.3 4 52 53 44 48 48 53 Table 12.17: Weight gains of rats.
Thyroxin Thiouracil Control 132 68 68 107 115 84 63 52 90 117 133 80 80 91 133 118 63 61 91 115 87 89 69 112 95 88 119

(c) Test for differences between all pairs of adhesive systems using α = 0.01 tests.

(d) Find the sums of squares i) for comparing system 1 with system 4 and ii) for comparing system 2 with system 3.

(e) Assuming that systems 1 and 4 have the same means and that systems 2 and 3 have the same means, perform a 0.01 level F test for whether the peel-strength of systems 1 and 4 differs from the peel-strength of systems 2 and 3.

(f) Give a 99% confidence interval for the mean of every adhesive system.
(g) Give a 99% prediction interval for every adhesive system.
(h) Give a 95% confidence interval for the difference between systems 1 and 2.