We found evidence for an interaction in the FatRats data after combining beef and pork into a single meat group; see the second ANOVA table in Table 7.9 on page 329. Later in that example we showed inferences for the effect of protein source (meat, cereal) conditional on protein quality (low, high). There is a second set of conditional inferences, for the effect of protein quality conditional on protein source. Parts (a) and (b) ask you to find and interpret these conditional intervals and effect sizes. The following summary numbers might be useful in doing so. For meat the cell means are 85.90 (high quality) and 83.90 (low quality) with sample sizes of 20 in each group. For cereal the cell means are 99.75 (high) and 79.05 (low) with sample sizes of 10 in each group. The mean square error from the ANOVA table is 206.6 with 56 degrees of freedom.

a. Construct and interpret the two confidence intervals for the effect of protein quality conditional on protein source.

b. Construct and interpret effect sizes for protein quality conditional on the protein source