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Solved by verified expert:In a one way ANOVA, the researcher compares two or more groups in order to come up with the average mean. For example, one can compare three classrooms to establish their mean. In a two way ANOVA, one compares two different categories (St & Wold, 1989). An excellent example of a two way ANOVA is the comparison of two different classes and genders in those classes and come up with the mean. In this research, I want to compare the mean of classes A, B, and C in Chicago Academy Secondary School at the same time compare the mean of both male and female in those classes. In my investigation, one variable dependent I would use is the mean score and two variables independent of the number of students and gender. In my research also, the total number of students in class A=40, the total number of students in class B=60 and the total number of students in class C=50.The reason I have chosen to investigate the two independent variables of gender and number of students in three classes in Chicago Academy is to find out how the individual classes perform at the same time I would like to find out how boys perform to girls. The investigation will affect the dependent variables in the sense that after the research, I would be able to know how classes differ in terms of performances and how gender varies in terms of performances. I would also be able to see the significance of the number of students in each class and gender on the mean score.The interactions that I expect from the above chosen independent variables would be interactions that would answer the following questions; which class does better in the test? Who between male and female performs better in the test? What is the significance of the combination of both class and gender? How does gender affect the mean score? How does the number of students in each class affect the mean score? The above interaction would change the dependent variable in that by the end of the interactions, I would have known how the two factors of the number of students in each class and gender affect the mean score.In conclusion, I predict that the mean of both the independent variables of the number of students in a class and gender have significance on the mean score. In my prediction, the males in class A performs high, female in class A score low while male in class A score low and their female counterparts score high. Male in class C performs high in their tests and their female counterparts score low in the same tests. In my prediction too, you cannot compare the mean in the three classes in the sense that, genders in all the three classes perform differently and again, the number of students in all the three classes are not the same.Ho1: There is no significant difference in the mean scores betweenthe three classesHo2: There is no significant difference in the mean scores betweenmales and femalesHo3: There is no interaction between the two independent variables ofclasses and genderHa1: There is a significant difference in the mean scores betweenthe three classesHa2: There is a significant difference in the mean scores betweenmales and femalesHa3: There is an interaction between the two independent variables ofclasses and genderReferencesSt, L., & Wold, S. (1989). Analysis of variance (ANOVA). Chemometrics and intelligent laboratory systems, 6(4), 259-272..

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