Questions Only — Exam I

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University of Nebraska, Lincoln *

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Statistics

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Feb 20, 2024

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Page 1 October 17, 2023 Project Statement © 2023 Society of Actuaries Exam PA October 17 Project Statement IMPORTANT NOTICE – THIS IS THE OCTOBER 17, 2023 PROJECT STATEMENT. IF TODAY IS NOT OCTOBER 17, 2023, SEE YOUR TEST CENTER ADMINISTRATOR IMMEDIATELY. General Information for Candidates This examination has 10 tasks numbered 1 through 10 with a total of 70 points. The points for each task are indicated at the beginning of the task, and the points for subtasks are shown with each subtask. Each task pertains to the business problem described below. Additional information on the business problem may be included in specific tasks—where additional information is provided, including variations in the target variable, it applies only to that task and not to other tasks. For this exam there is no data file or .Rmd file provided. Neither R nor RStudio are available or required. The responses to each specific subtask should be written after the subtask and the answer label, which is typically ANSWER, in this Word document. Each subtask will be graded individually, so be sure any work that addresses a given subtask is done in the space provided for that subtask. Some subtasks have multiple labels for answers where multiple items are asked for—each answer label should have an answer after it. Each task will be graded on the quality of your thought process (as documented in your submission), conclusions, and quality of the presentation. The answer should be confined to the question as set. No response to any task needs to be written as a formal report. Unless a subtask specifies otherwise, the audience for the responses is the examination grading team and technical language can be used. Prior to uploading your Word file, it should be saved and renamed with your five-digit candidate number in the file name. If any part of your exam was answered in French, also include “French” in the file name. Please keep the exam date as part of the file name. The Word file that contains your answers must be uploaded before the five-minute upload period time expires.

Page 2 October 17, 2023 Project Statement © 2023 Society of Actuaries Business Problem You are a consultant and your client has asked you to perform a study related to outcomes in university in the United States. Your client is interested in better understanding the drivers of several key variables and developing models to predict them. These target variables include: • tuition prices • students who are defaulting on student loans • future earnings of students • student loan repayment rates • university admission rates To answer these questions, you decide to use a publicly available dataset 1 that includes aggregated data from 2,180 universities in the United States for the 2020-2021 school year. 1 Source: United States Department of Education

Page 3 October 17, 2023 Project Statement © 2023 Society of Actuaries Data Dictionary Variable Data Type: Range/Levels Description UNITID Numeric : 100654 to 495767 ID for the institution INSTNMH String: N/A Institution name REGION Factor: 10 levels Region (IPEDS) CONTROL Factor: 3 levels (“Public”, “Private, non-profit”, ”Private, for-profit”) Control of institution LOCALE Factor: 4 levels (“City”, “Suburb”, ”Town”, ”Rural”) Locale of institution ADMIT_TIER Factor: 5 levels ("MOST SELECTIVE", "EXTREMELY SELECTIVE", "VERY SELECTIVE", "MODERATELY SELECTIVE", "NOT SELECTIVE") How selective the institution is TEST_REQ Factor: 4 levels ("Required", "Recommended", "Neither required nor recommended", "Considered but not required") Does the institution require standardized tests ADM_RATE Numeric : 0.0244 to 1.0 Admission rate SATVRMID Numeric: 395 to 760 Midpoint of SAT critical reading scores SATMTMID Numeric: 350 to 795 Midpoint of SAT math scores SATWRMID Numeric: 280 to 765 Midpoint of SAT writing scores UGDS Numeric: 2 to 109,233 Number of undergraduate certificate/degree-seeking students SCHOOL_SIZE Factor: 3 levels (“Small”, “Medium”, ”Large”) The size of the university based on number of students TUITIONFEE_IN Numeric: 480 to 61,671 In-state tuition and fees TUITIONFEE_OUT Numeric: 480 to 61,671 Out-of-state tuition and fees

Page 4 October 17, 2023 Project Statement © 2023 Society of Actuaries AVGFACSAL Numeric: 547 to 21,143 Average faculty salary per month PFTFAC Numeric: 0.0339 to 1.0 Proportion of faculty that is full-time PCTPELL Numeric: 0.0054 to 1.0 Percentage of undergraduates who receive a Pell Grant PCTFLOAN Numeric: 0.0015 to 1.0 Percent of undergraduate students receiving a federal student loan MD_EARN_WNE_P10 Numeric: 13,438 to 132,969 Median earnings of students working and not enrolled 10 years after entry COMPL_RPY_7YR_RT Numeric: 0.2059 to 0.9814 Seven-year repayment rate for completers NONCOM_RPY_7YR_RT Numeric: 0.1130 to 0.9314 Seven-year repayment rate for non- completers GRAD_DEBT_MDN Numeric: 2,334 to 48,148 The median debt for students who have completed WDRAW_DEBT_MDN Numeric: 2,352 to 24,167 The median debt for students who have not completed COSTT4_A Numeric: 5,663 to 81,531 Average cost of attendance CDR3 Numeric: 0.001 to 0.357 Three-year cohort default rate LOAN_EVER Numeric: 0.0139 to 0.9856 Percent of students who received a federal loan while in school AGE_ENTRY Numeric: 17.43 to 51.60 Average age of entry into the institution FEMALE Numeric: 0.04156 to 0.97957 Share of female students MARRIED Numeric: 0.0027 to 0.8154 Share of married students FIRST_GEN Numeric: 0.08867 to 0.85091 Share of first-generation students MD_FAMINC Numeric: 1,680 to 179,864 Median family income

Page 5 October 17, 2023 Project Statement © 2023 Society of Actuaries Task 1 (5 points ) Your client wants to understand the factors influencing university admission rates. Your client is interested in ensuring that the analysis has proportional representation with respect to different regions of the country ( REGION ) and population densities ( LOCALE ). (a) ( 3 points ) Describe the steps for developing a stratified sample based on your client’s goals. ANSWER: Your client is also interested in student opinions about the university. You are given a dataset with written responses to a university satisfaction survey. (b) ( 2 points ) Discuss the advantages and disadvantages of using this kind of unstructured data in a predictive model. ANSWER:

Page 6 October 17, 2023 Project Statement © 2023 Society of Actuaries Task 2 (11 points ) Your assistant is interested in understanding the relationship between the features admission rate ( ADM_RATE ) and in-state tuition ( TUITIONFEE_IN ) and is considering whether to perform a K-means analysis or a hierarchical clustering analysis to better understand the relationship. (a) ( 4 points ) Describe two similarities and two differences between K-means clustering and hierarchical clustering. ANSWER: Your assistant prepared an elbow plot of K-means clustering using the in-state tuition ( TUITIONFEE_IN ) and admission rate ( ADM_RATE ) features, shown below. (b) ( 3 points ) Explain the tradeoff between selecting a value of K=2 and K=4. Recommend a value for K and justify your recommendation. ANSWER:

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