Reconsider the experiment of Exercise 13-5. Suppose that the experiment was conducted as a RCBD with blocks formed by days (denoted as columns in the data table). In the experiment, the primary interest is still in the effect of cotton percentage and day is considered a nuisance factor.

(a) Consider day as a block, and re-estimate the ANOVA.

(b) Does cotton percentage still affect strength at α = 0.05?

(c) Compare the conclusions here with those obtained from the analysis without blocks.

Exercise 13-5

In Design and Analysis of Experiments, 8th edition (John Wiley & Sons, 2012), D. C. Montgomery described an experiment in which the tensile strength of a synthetic fi ber was of interest to the manufacturer. It is suspected that strength is related to the percentage of cotton in the fiber. Five levels of cotton percentage were used, and five replicates were run in random order, resulting in the following data.

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Observations Cotton Percentage 2 3 15 15 11 20 12 17 12 18 18 25 14 18 18 19 19 30 19 25 22 19 23 35 10 11 15 11