A researcher is interested in examining how teachers' expectations of their students' scholastic abilities might affect students' self-perceptions of their own ability and whether this effect varies as a function of a student's age. She has a sample of teachers rate their students as having either low or high expectations of success; these teachers are from the first, third, and fifth grades. She then has students rate their own abilities on a scale of 1 (low) to 15 (high). She hypothesizes that students with low expectations by the teacher would display lower ratings of their own ability than students with high teacher expectations. Furthermore, she believes this difference will increase as students progress through the educational system, growing larger from first to third to fifth grade. Below are descriptive statistics of students' ratings of their ability.

a. Create a figure to represent the cell means.

b. Conduct the two-way ANOVA and create an ANOVA summary table.

c. Report the decisions regarding the null hypotheses and the level of significance for the main effects and the interaction effect.

d. Calculate measures of effect size \(\left(R^{2}\right)\) for the main effects and the interaction effect.

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Grade (Factor A): First First Third Third Fifth Fifth Expectation (Factor B): Low High Low High Low High NAB 3 3 3 3 3 3 Mean (AB) 5.00 6.33 3.67 8.67 2.33 9.67 Standard deviation (SAB) 1.00 1.53 1.53 1.53 1.15 1.53