The strength of paper depends upon the length and other characteristics of the wood fiber stock entering the paper machine. Consequently, as the source of the fiber stock varies over time, we expect the strength of the produced paper to vary also. To test this theory, 6 days were randomly selected from within a 4-month period of time. On each of these days, an end-of-the-roll paper patch was selected from each of three randomly selected rolls. Two strength tests were conducted on each of the 18 patches of paper. The strength measurements (pounds per square inch) are shown in the table.

a. Perform an analysis of variance for the data using the formulas provided in this section. Construct an analysis of variance table to display the results.

b. Do the data provide sufficient evidence to indicate that the variation in paper strength between days exceeds the variation within days? Test using α = .05.

c. Do the data provide sufficient evidence to indicate that the variation in strength from roll to roll exceeds the variation between strength tests within a roll? Test using α = .05.

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WOODFIBER Day 2 3 4 6 1 20.7 22.1 19.0 20.6 23.2 20.7 19.3 20.4 19.9 18.9 22.5 18.5 Rolls 2 21.2 21.6 18.8 19.8 24.2 19.6 Within Days 20.1 22.5 19.3 20.1 22.9 21.3 3 19.9 20.9 20.2 20.7 23.4 20.0 20.5 22.1 19.4 19.2 24.6 18.6