Problem Set 1: (22 pts) A teacher wanted to see if a new pedagogical approach was beneficial to students, and if the effects vary by amount math anxiety. To examine this, students completed math anxiety surveys and were grouped into "low", "average", and "high" levels of math anxiety. She then randomly assigned equal numbers of students from each group into one of two classes - one taught using her "standard" approach; the other class was taught using a new approach. The data presented in the table below are the final grade percentages of the 60 children (30 per class). Conduct the most appropriate statistical analysis to determine whether final grades in a math class were affected by teaching approach and/or amount of math anxiety. Low Final grade (%) Standard 72 Average | High 80 approach 77 68 85 73 71 73 75 73 81 69 97 73 73 90 91 74 95 73 88 76 73 67 89 71 97 81 75 New 75 78 approach 89 68 90 79 93 89 58 89 88 79 83 75 81 88 80 69 92 86 86 91 88 88 94 85 81 87 77 68