Question: Based on teacher assessments, an experimenter has divided 100 students into two groups, one judged to have a high self-esteem and one judged to have a low self esteem. The experimenter administers a survey of common fears to the two groups of students. She arbitrarily decides that a score of 1 to 10 on the scale indicates a low number of fears, 11 to 20 a moderate number of fears, and 21 to 30 a high number of fears. For the low self-esteem group, she finds that 10 fall into the low category, 15 fall into the moderate category, and 25 fall into the high category. The results for the high self-esteem group are just the opposite: 25 students are in the low category, 15 in the moderate category, and 10 in the high category. Perform a chi-square test of independence to see whether high and low self-esteem students differ on the fear survey.