Return to the rubber stress data in Table 10.6. The statistician who performed the analysis in Example 10.3 reasoned “the more data the better,” and kept the analysis as presented. Overnight, she had...

Return to the rubber stress data in Table 10.6. The statistician who performed the analysis in Example 10.3 reasoned “the more data the better,” and kept the analysis as presented. Overnight, she had second thoughts, and decided “more stable data would be better, so perhaps I should average the four measurements within each lab/material, and submit this to a randomized block analysis.”

(a) Demonstrate that she will obtain the same F test for material as originally presented for Example 10.3.

(b) Explain why, using the expected mean squares in Table 10.5.

Example 10.3

We are interested in the stretching ability of different rubber materials as measured by stress at 600% elongation of the materials. Since different testing laboratories often produce different results, four samples of each of seven materials were sent to a sample of 13 laboratories Mandel (1976). The data are given in Table 10.6.