A study of the difference in the effects of six newly created diets on the weight gain of young rabbits is proposed. Because weight varies considerably amongst young rabbits, it is proposed to block the experiment based on litters. There are 10 litters of rabbits available for the study, but they are of varying sizes. The minimum litter size is three. Therefore, only three of the six diets can be observed in any particular litter. A balanced incomplete block design was proposed for this situation. The researcher conducted the study and obtained the following weight gains.

Do the data provide significant evidence of a difference in mean weight gains amongst the six diets? Use the formulas given in this Section 19.4 to obtain your answers.

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Litter 32.6 35.2 40.1 381 40.9 4 8 40.9 37.3 32.0 45.2 40.6 9 Diet total 215 179.2 195.5 182.5 1724 212.9 1154.0 Diet mean 423 35.84 39.1 36.5 34.48 42.58