4. (Taken from Rao 16.8, p. 765) An experiment evaluates the taste of three brands of ice cream under different storage conditions. The expt. calls for 12 coolers to be randomized to the 3 brands (4 coolers per brand). Within each cooler, there is room for three half-gallon cartons of ice cream, all from the same brand. One carton was sampled at random at the end of one day, then at the end of one week and then one month. Each carton was evaluated for flavor by a panel of tasters. These panel scores can be found in the file entitled "icecreamstorage.dat". (a) This is a split-plot experiment. What are the whole plot units? (b) What is/are the whole plot factor(s)? (c) What is/are the sub plot factor(s)? (d) Test for an interaction between storage time and brand. (Use a = 0.05.) (e) Test for main effects of storage time. Carry out pairwise comparisons among the three storage time tastes, using a Bonferroni correction to control the exptwise error rate at .05. (f) Test for main effects of brand. Report the standard error on any pairwise difference among brands. (g) Suppose you had averaged the data over storage time, reducing the total number of observations from 36 down to 12. Would the F-ratio for brand effect in a a one-way ANOVA be the same as the F-ratio from part (g)? Try it and see