Explanation Calculation: The given information is that there are three sizes of bass and two different species of prey. The sum of squares for size, species, interaction, and total are 0.088, 0.048, 0.048, and 0.316, respectively. Here, the number of treatments ( k ) is 3, the number of blocks ( l ) is 2, and the number of observations in each combination ( m ) is 3. The degrees of freedom for Size is calculated as follows: d f = k − 1 = 3 − 1 = 2 The degrees of freedom for Species is calculated as follows: d f = l − 1 = 2 − 1 = 1 The degrees of freedom for Interaction is calculated as follows: d f = ( k − 1 ) ( l − 1 ) = ( 3 − 1 ) ( 2 − 1 ) = 2 × 1 = 2 The degrees of freedom for Error is calculated as follows: d f = k l ( m − 1 ) = 3 × 2 × ( 3 − 1 ) = 3 × 2 × 2 = 12 The degrees of freedom for Total is calculated as follows: d f = k l m − 1 = ( 3 × 2 × 3 ) − 1 = 18 − 1 = 17 The value of sum of squares for error is calculated as follows: SSTo = SSA + SSB + SSAB + SSE , Here, SSTo is the total sum of squares, SSA is the sum of squares for treatments, SSB is the sum of squares for blocks, SSAB be the sum of squares for interaction, and SSE is the sum of squares for error. SSE = SSTo − SSA − SSB − SSAB = 0.316 − 0.088 − 0.048 − 0.048 = 0.132 Here, MSA be the mean sum of square for Size, MSB be the mean sum of square for Species, MSAB be the mean sum of squares for interaction, and MSE be the mean sum of squares for error. The value of mean sum of squares for Size is calculated as follows: MSA = SSA d f for Size = 0.088 2 = 0.044 The value of mean sum of squares for Species is calculated as follows: MSB = SSB d f for Status = 0.048 1 = 0.048 The value of mean sum of squares for Interaction is calculated as follows: MSAB = SSAB d f for Interaction = 0.048 2 = 0.024 The value of mean sum of squares for Error is calculated as follows: MSE = SSE d f for Error = 0.132 12 = 0.011 Here, F A be the test statistic for Size, F B be the test statistic for Species, and F A B be the test statistic for Interaction. The value of F test statistic for Size is calculated as follows: F A = MSA MSE = 0.044 0.011 = 4 The value of F test statistic for Species is calculated as follows: F B = MSB MSE = 0

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Test all appropriate hypotheses using 0.01 level of significance.

Solution Summary: The author explains that there is no interaction between Size and Species, and no evidence that the preference index depends on size.

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