Internet addiction has been found to be a widespread problem among university students. A small liberal arts college in Colorado conducted a survey of Internet addiction among its students using the Internet Addiction Test (IAT) developed by Dr. Kimberly Young. The IAT measures three underlying psychometric factors: emotional/psychological conflicts (Factor1), time management issues (Factor2), and mood modification (Factor3). Individuals who score high on the IAT are more likely to have problematic Internet use. The accompanying table shows a portion of the scores for the three psychometric factors for 350 students. The respondents also provided a couple of pieces of demographic data including sex (equals 1 if female, 0 otherwise) and level of study (equals 1 if graduate study, 0 otherwise). 

a. Perform hierarchical clustering to group the 350 university students using the three psychometric factors as well as the other demographic variables. Use Gower’s coefficient for the distance between observations and Ward’s clustering method to cluster the students into three clusters. How many students are in the largest cluster? 

b. What are the average scores for emotional/psychological conflicts, time management issues, and mood modification for students in the largest cluster?

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Record Factor1 1.44 2.44 ⠀ 1.33 1 2 E 350 Factor2 2.40 2.80 B 2.20 : E : ⠀ Graduate 1 0 E 0