Exercise 5 The psychology department at a hypothetical university has been accused of underpaying female faculty members. The following data represent salary (in thousands of dollars) for every assistant professor and associate professor in the department. I: Female Assistant Professors II: Male Assistant Professors III: Female Associate Professors IV: Male Associate Professors Group I II III IV 33 36 38 40 40 35 40 44 49 38 44 43 47 42 48 37 51 48 45 (a) Fit a two-way ANOVA model entering gender (Male, Female) as Factor A and rank (Assistant, Associate) as Factor B. Is the interaction of gender and rank significant? (b) Write the null and alternative hypotheses for testing the main effect of gender using Type I, Type II, and Type III sums of squares. Report the full and reduced models that correspond to each test