\f16. Felix measured participants' preferences for two brands of soft drinks (factor A). For each brand he tested male and female participants (factor B). The ANOVA produces all significant Fs. The MS = 9.45, n = 11 per cell, and of = 40. The means are below. Factor A Level A : Level A,: Brand X Brand Y Level B: Males 14 29 21.5 Factor B Level B,: 25 12 18.5 Females 19.5 20.5 (a) What are the main effect means for brands? Describe this main effect on preferences. (b) What are the main effect means for gender? Describe this main effect on preferences. (c) Perform Tukey's HSD test where appropriate. (d) Describe the interaction. (e) Describe a graph of the interaction when factor A is on the X axis. (f) Why does the interaction contradict your conclusions about the main effects?17. Below are the cell means of three experiments. For each, compute the main effect means and decide whether there appears to be an effect of A, B, and/or A X B. Study 1 Study 2 Study 3 A, A 2 10 5 14 12 14 5 10 2 18. In question 17, if you label the X axis with factor A and graph the cell means, what pattern will you see for each interaction?20. You measure the dependent variable of participants' relaxation level as a function of whether they meditated before being tested, and whether they were shown a film containing a low, medium, or high amount of fantasy. Here are the data and the ANOVA. Amount of Fantasy Low Medium High Mediation 10 10 NWAUNUSOON 10 10 No Mediation 9 10 10 Sum of Mean Source Squares dif Square A: Fantasy 42.467 2 21.233 13.134 B: Meditation 833 1 833 515 A X B: Interaction 141.267 2 70.633 43.691 Within 38.800 24 1.617 Total 223.367 29 (a) Which effects are significant? (b) Compute the main effect means and the interactionmeans. (c) Perform the Tukey HSD test where appropriate. (d) What do you conclude about the relationship(s) this study demonstrates? (e) Evaluate the impact of each effect