In the book Design of Experiments for the Quality Improvement published by the Japanese Standards Association (1989), a study on the amount of dye needed to get the best color for a certain type of a fabric was conducted. The three amounts of dye, 1/3% wof (1/3% of the weight of a fabric), 1% wof, and 3% wof, were each administered at two different plants. The color density of a fabric was then observed four times for each level of dye at each plant. Perform an analysis of variance to test the hypothesis, at the 0.05 level of significance, that there is no difference in the color density of a fabric for the three levels of dye. Consider plants to beblocks.

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Amount of Dye 1/3% 6.0 12.3 5.2 12.4 5.9 5.9 5.5 14.5 5.9 6.4 3% Plant 1 22.4 17.8 10.9 22.5 11.8 29.0 29.7 Plant 2 6.5 23.2 13.6 16.0 24.0