A researcher is interested in the effect of four diets on the weight gain of newborn rats. The researcher randomly assigns rats from the same mother to each treatment so that a set of four rats constitutes a block. In blocking by mother, we are removing any variability in weight gain due to genetic differences. The researcher identifies five mother rats that each had four offspring, for a total of 20 rats. For each block (sibling rats), the researcher randomly assigns the experimental units (rats) to a treatment using randomly generated integers from 1 to 4 . After six months, she records the weight gain of the 20 rats (in grams) and obtains the data in Table 10. Is there sufficient evidence to conclude that the weight gains of the rats on the four diets differ at the \(\alpha=0.05\) level of significance?

Approach Verify the requirements for analyzing data from a randomized complete block design are satisfied and then analyze the results of the experiment using Minitab. The steps for performing a randomized complete block design using Minitab and StatCrunch are given in the Technology Step-by-Step.

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Table 10 Diet 1 Diet 2 Diet 3 Diet 4 Block 1 15.0 14.6 17.7 10.4 Block 2 17.9 17.4 16.0 12.2 Block 3 17.5 14.8 14.2 14.8 Block 4 16.3 17.3 14.4 12.0 Block 5 15.4 19.3 18.8 14.3