Module 3 Critical Thinking Attempt 2 MTH156-3

Graduation and Publication Probabilities Colorado State University Global MTH156-3: Introduction to Statistics Dr. Rudilee Gabel January 8 th , 2023 1

2 Graduation and Publication Probabilities Probability is a measure used to determine the likelihood of a specific event occurring within an experiment with a numerical value between zero and one. The probability of a specific event can be determined using one of three methods, the classical approach, the relative frequency approach (also known as empirical probability), and the subjective approach. The classical approach is the theoretical probability of an event occurring considering there are equally likely outcomes, and is derived by simply taking the number of possible outcomes that the event occurs and dividing by the total number of possible outcomes. The empirical probability or relative frequency approach represents the probability of an event happening in a large number of trials and is determined by taking the number of trials in which the event occurs and dividing by the total number of trials. Lastly, the subjective approach is based on assumption and reflects the extent to which it is assumed that the event will or will not occur. For this study we will analyze the data from three universities, each with a specified group of instructors, the number of students who graduated, and how many students had their work published. The universities that we have data for are WWCC (14 professors), EWCC (13 professors), and NWCC (13 professors). To better analyze the data provided, we will determine and pay special attention to probabilities of graduation and publication. Using those probabilities we will rank professors at each university as well as each university as a whole. Overall Probabilities for each University To start, we will determine the overall probability of students graduating from each of the three universities. To calculate this, we will simply take the total number of students that graduated and divide by the total number of students. The probability for each university is as follows: WWCC overall probability of students graduating : 15,658  17,921 = 0.87372

4 = 0.39466 NWCC overall probability of students graduated with a publication: 0.31019  0.89594 = 0.34621 The conditional probabilities derived for each university, reflect that it is more likely that students that graduated and had their work published were from WWCC (0.40266) versus students from NWCC (0.34621). Ranking of Professors Based on Graduation Probabilities The next thing to determine is the probability of a student graduation for each professor at all three universities, as well as how each professor ranks for the college. To compute this we will divide the number of students that graduated by the total number of students taught by each professor. The probabilities are displayed in the column labeled P(Graduated) and the rank for each professor is in column Rank by P(G). WWCC: Based on the probability of students that graduated for each professor, we were able to rank the professors one to thirteen given the fact that two professors had a graduation rate of 100%. Both professors D.K. Raulson and E.A. Thomas tied for first in the rankings while the lowest ranking went to T.R. South. Professor/WWCC Number Students Taught Graduated P(Graduated) Rank by P(G) J.W. Blake 264 256 0.96969 4 K.R. Cunningham 751 593 0.78961 11 R.H. Doughty 1724 1448 0.83990 9 L.M. Edwards 236 227 0.96186 5 W.H. Greiner 1574 1275 0.81003 10 I.D. Jackson 1527 1512 0.99017 2 O.P. Lawson 1888 1454 0.77012 12

5 G.F. Nelson 915 796 0.86994 7 A.F. Paul 1892 1854 0.97991 3 D.K. Raulson 2611 2611 1 1 T.R. South 2852 2139 0.75 13 E.A. Thomas 261 261 1 1 C.F. Viney 1295 1114 0.86023 8 F.E. Yousef 131 118 0.90076 6 EWCC: Considering the probability of students that graduated for each professor, they are ranked from one to twelve although there are thirteen professors. Based on these ranks we can see that like WWCC, there are two professors that had a 100% graduation rate and those professors were S.D. Gundel and K.G. Ross. Looking at these rankings we can additionally see that the instructor with the lowest graduation rate was W.M Kraft. Professor/EWCC Number Students Taught Graduated P(Graduated) Rank by P(G) A.D. Blaise 667 634 0.95052 6 I.A. Frank 1417 1105 0.77981 11 S.D. Gundel 2200 2200 1 1 P.O. Hogan 1282 1231 0.96021 4 W.M. Kraf 2082 1582 0.75984 12 L.I. Luebbers 554 537 0.96931 3 J.H. Nye 292 237 0.81164 9 J.A. O'Dell 1161 1126 0.96985 2 R.W. Pauly 1873 1611 0.86011 7 K.G. Ross 382 382 1 1 D.S. Smith 545 447 0.82018 8 J.P. Trost 1380 1325 0.96014 5 M.M. Wall 399 315 0.78947 10

7 WWCC: Based on the computations made for WWCC, we can see that students taught by professor A.F. Paul are most likely to have their work published whereas the students for W.H. Greiner are least likely as this professor has the lowest probability. Professor/WWCC Number Students Taught Publications P(Publications) Rank by P(P) J.W. Blake 264 64 0.24242 13 K.R. Cunningham 751 190 0.25299 11 R.H. Doughty 1724 550 0.31902 8 L.M. Edwards 236 64 0.27118 10 W.H. Greiner 1574 319 0.20266 14 I.D. Jackson 1527 711 0.46561 2 O.P. Lawson 1888 683 0.36175 5 G.F. Nelson 915 231 0.25245 12 A.F. Paul 1892 908 0.47991 1 D.K. Raulson 2611 966 0.36997 4 T.R. South 2852 941 0.32994 7 E.A. Thomas 261 91 0.34865 6 C.F. Viney 1295 546 0.42162 3 F.E. Yousef 131 41 0.31297 9 EWCC: Based on the rankings for students being published per professor, we can see that students had a higher probability of being published under instructor K.G. Ross. Students with professor I.A. Frank were least likely to have their work published. Professor/EWCC Number Students Taught Publications P(Publications) Rank by P(P)

8 A.D. Blaise 667 292 0.43778 4 I.A. Frank 1417 276 0.19477 13 S.D. Gundel 2200 792 0.36 8 P.O. Hogan 1282 616 0.48049 2 W.M. Kraf 2082 649 0.31171 11 L.I. Luebbers 554 252 0.45487 3 J.H. Nye 292 107 0.36643 7 J.A. O’Dell 1161 405 0.34883 10 R.W. Pauly 1873 532 0.28403 12 K.G. Ross 382 187 0.48952 1 D.S. Smith 545 215 0.39449 6 J.P. Trost 1380 557 0.40362 5 M.M. Paul 399 145 0.36340 9 NWCC: The probabilities of students being published based on their professor for NWCC are not overly high. The instructor with the highest rank for this category was M.A. Carter. The professor that received the lowest ranking was M.P. Drake. Professor/NWCC Number Students Taught Publications P(Publications) Rank by P(P) D.H. Allen 2658 677 0.25470 8 T.G. Black 2879 710 0.24661 9 M.A. Carter 1126 529 0.46980 1 M.P. Drake 984 199 0.20223 13 J.K. Elmsworth 215 47 0.21860 12 P.T. Grey 1691 392 0.23181 10

10 K.R. Cunningham 593 190 0.32040 10 R.H. Doughty 1448 550 0.37983 6 L.M. Edwards 227 64 0.28193 12 W.H. Greiner 1275 319 0.25019 13 I.D. Jackson 1512 711 0.47023 3 O.P. Lawson 1454 683 0.46973 4 G.F. Nelson 796 231 0.29020 11 A.F. Paul 1854 908 0.48975 2 D.K. Raulson 2611 966 0.36997 7 T.R. South 2139 941 0.43992 5 E.A. Thomas 261 91 0.34865 8 C.F. Viney 1114 546 0.49012 1 F.E. Yousef 118 41 0.34745 9 EWCC: Based on the computations for the graduated students that had their work published per professor at EWCC, we can see that the students of P.O. Hogan had the highest probability of publications while students of I.A. Frank had the lowest probability. Professor/EWCC Graduated Publications P(P|G) Rank by P(P|G) A.D. Blaise 634 292 0.46056 5 I.A. Frank 1105 276 0.24977 13 S.D. Gundel 2200 792 0.36 10 P.O. Hogan 1231 616 0.50040 1 W.M. Kraf 1582 649 0.41024 9 L.I. Luebbers 537 252 0.46927 4 J.H. Nye 237 107 0.45147 7

11 J.A. O’Dell 1126 405 0.35968 11 R.W. Pauly 1611 532 0.33022 12 K.G. Ross 382 187 0.48952 2 D.S. Smith 447 215 0.48098 3 J.P. Trost 1325 557 0.42037 8 M.M. Wall 315 145 0.46031 6 NWCC: The probabilities found for graduated students who had their work published at NWCC per professor were slightly different than the others. At this university, there are two professors that ranked first in this category: M.A. Carter and B.M. Keith. The lowest ranking professor in this category was J.K. Elmsworth. Professor/NWCC Graduated Publications P(P|G) Rank by P(P|G) D.H. Allen 2605 677 0.25988 11 T.G. Black 2447 710 0.29015 7 M.A. Carter 1058 529 0.5 1 M.P. Drake 738 199 0.26964 9 J.K. Elmsworth 189 47 0.24867 12 P.T. Grey 1353 392 0.28972 8 C.R. Heines 1153 392 0.33998 6 D.R. Jones 680 252 0.37058 4 B.M. Keith 2050 1025 0.5 1 G.H. Matheson 338 132 0.39053 3 P.R. Neighbors 461 120 0.26030 10

13 P.O. Hogan 7 11 W.M. Kraf 32 2 L.I. Luebbers 10 10 J.H. Nye 23 5 J.A. O'Dell 23 5 R.W. Pauly 31 3 K.G. Ross 4 12 D.S. Smith 17 8 J.P. Trost 18 7 M.M. Wall 25 4 Professor/NWCC Sum of Ranks Overall Rank D.H. Allen 21 7 T.G. Black 26 5 M.A. Carter 6 12 M.P. Drake 35 1 J.K. Elmsworth 33 2 P.T. Grey 29 3 C.R. Heines 20 8 D.R. Jones 15 9 B.M. Keith 8 11 G.H. Matheson 10 10 P.R. Neighbors 28 4 S.T. Orion 6 12 A.P. Tracey 24 6

14 Conclusion Looking at the overall rankings for each professor and university can be useful information for potential students who are on the hunt for the right college. These rankings additionally reflect the graduation rates and likelihood of having their work published. At WWCC, the overall top three ranking professors are W.H. Greiner, K.R. Cunningham, and J.W. Blake. The overall top three ranking professors for EWCC are I.A. Frank, W.M. Kraft, and R.W. Pauly. Lastly, the top three overall professors at NWCC are M.P. Drake, J.K. Elmsworth, and P.T. Grey. Using the variety of probabilities computed above, we can make an informed decision and determination of what university and professor is best.