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 contains 20 questions that measure three underlying psychometric factors. Questions 1 through 9 measure emotional/psychological conflicts, which refer to the degree to which the individual uses the Internet as a means to avoid interactions with friends and family. Questions 10 through 14 measure time management issues, which refer to the degree to which the individual chooses to spend time online at the expense of other responsibilities. Finally, Questions 15 through 20 measure mood modification, which refers to the degree to which the individual’s Internet dependence is motivated by the need for mood improvement. The accompanying table shows a portion of the responses from 350 students. Students respond on a scale of 1 to 5, where higher values are indicative of possible problematic Internet use.

a. The scores for the three psychometric factors (i.e., emotional/psychological conflicts, time management issues, and mood modification) can be calculated by averaging the scores for the questions that are designed to measure them. First, find the average score for each psychometric factor for each student. Then, perform agglomerative clustering to group the 350 university students into five clusters based on the three underlying psychometric factors. Use Euclidean distance and the single linkage clustering method. Do not standardize the variables. 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 1 2 ⠀ 350 IAT 1 22 2 2 ⠀ 1 IAT2 2 3 ⠀ 2 ⠀ IAT20 1 1 ⠀ 1