please review the Case Study below and submit answers

Real Estate World: Real Estate World is trying to improve their selection process for hiring real estate agents. A successful real estate agent, according to the company, is one that can sell a minimum of 50 houses per year. The company believes that the key to successful real estate is perseverance. To test this hypothesis the company administers The Perseverance Assessment (TPA) to 75 applicants holding a proper real estate license. The company hires all of the applicants that scored higher than 3 on the TPA and gives all of them one year to see how they perform on the job. Given below are applicant scores on the TPA as well as how many houses each sold in the year. Answer the questions that follow.

TPA score # houses sold in the year

10 78 67 65 59 55

9 79 61 61 61 58 56 56 50 48 47

8 69 65 64 63 59 56 50 50 50 49 45 44 42 41 31

7 72 66 56 55 54 53 52 51 51 51 50 43 42 33 21

6 62 61 60 59 52 49 48 45 44 43 42 40 40 29 20

5 55 52 51 50 50 43 41 33 29 18

4 57 49 40 27 22

Provide definition and numeric answers for the following questions.

Questions:

  1. If 150 applicants scored 3 or lower on the TPA and thus were not hired, what was the selection ratio for this job?
  2. If 50 houses sold per year is the criterion for success, what is the base rate for real estate agents with Real Estate World?
  3. If the company decides to use 8 as the passing score on the test, how many:
  • True positives? _____
  • False positives? _____
  • True negatives? _____
  • False negatives? _____
  1. What percentage of the 75 employees were correct selection decisions, and what percentage were incorrect decisions. What do these results suggest about the value of the TPA test to select real estate agents?
  2. Briefly describe the pros & cons to using a cut score for selection based on these results.