In the following study, three different universities have been tracking a select

Question

In the following study, three different universities have been tracking a select group of professors over the course of their employment at that university to determine the number of students who are in a particular professor’s classes, how many of those students have graduated and if any of them have had their work published. In the attached Excel file Probabilities are the totals for each of the professors at the three different universities that participated in the study.

The purpose of this study is to find the probabilities of graduation and publication for the students in the different professors’ courses. While a causal relationship may not be found between a professor and student graduation or publication, we need to rank the professors based on the different probabilities found with the data sets as described below.

Prepare a report (see below) with your ranking of the professors based on the probabilities and conditional probabilities as well as the analysis of each university. Include the following seven (7) items in table format which is provided in the Probabilities file to support your ranking.

NOTE: Be sure to use five (5) decimal places for your probabilities in the table, as some of them will be quite small.

The overall probability of students graduating at each of the three universities.

The overall probability of students having a publication at each of the three universities.

The overall probability of students having a publication, given that they graduated at each of the three universities.

The probability of a student graduating for each professor.

The probability of a student having a publication for each professor.

The probability of a student having a publication given that they graduated for each professor.

Rank the professors within each university for each of the probabilities in 4 - 6. Then find the sum of the ranks and determine an overall ranking for each professor.

University/College Professor/Instructor Number Students Taught Graduated Publications P(Graduated) Rank by P(G) P(Publications) Rank by P(P) P(P|G) Rank by P(P|G) Sum of Ranks Overall Rank WWCC J.W. Blake 2541 2134 704 K.R. Cunningham 2378 1831 842 R.H. Doughty 1942 1864 615 L.M. Edwards 1044 1002 411 W.H. Greiner 2219 2152 882 I.D. Jackson 2243 2198 659 O.P. Lawson 874 874 219 G.F. Nelson 1202 1118 559 A.F. Paul 1199 995 279 D.K. Raulson 597 496 233 T.R. South 1702 1345 551 E.A. Thomas 2422 2180 567 C.F. Viney 1724 1293 388 F.E. Yousef 980 804 209 Totals EWCC A.D. Blaise 905 688 275 I.A. Frank 1667 1467 719 S.D. Gundel 2374 1899 741 P.O. Hogan 392 298 116 W.M. Kraft 1998 1938 620 L.I. Luebbers 1357 1194 490 J.H. Nye 129 111 48 J.A. O'Dell 953 896 287 R.W. Pauly 2229 1962 785 K.G. Ross 2808 2331 1049 D.S. Smith 2812 2250 765 J.P. Trost 1095 898 225 M.M. Wall 1745 1571 754 Totals NWCC D.H. Allen 333 303 124 T.G. Black 1422 1081 400 M.A. Carter 360 310 90 M.P. Drake 2636 2241 1053 J.K. Elmsworth 739 554 244 P.T. Grey 1848 1515 651 C.R. Heines 1985 1826 548 D.R. Jones 1417 1332 386 B.M. Keith 2824 2570 848 G.H. Matheson 1495 1375 688 P.R. Neighbors 2652 2307 969 S.T. Orion 1310 1205 374 A.P. Tracey 1146 928 316 Totals

Explanation / Answer

University/College Professor/Instructor Number Students Taught Graduated Publications P (Graduated) Rank by P(G) P (Publications) Rank by P(P) P (P|G) Rank by P(P|G) Sum of Ranks Overall Rank WWCC J.W. Blake 2541 2134 704 0.83983 8 0.27706 9 0.32990 8 25 10 K.R. Cunningham 2378 1831 842 0.76997 13 0.35408 5 0.45986 3 21 7 R.H. Doughty 1942 1864 615 0.95984 4 0.31668 7 0.32994 7 18 5 L.M. Edwards 1044 1002 411 0.95977 5 0.39368 3 0.41018 4 12 3 W.H. Greiner 2219 2152 882 0.96981 3 0.39748 2 0.40985 5 10 2 I.D. Jackson 2243 2198 659 0.97994 2 0.29380 8 0.29982 10 20 6 O.P. Lawson 874 874 219 1.00000 1 0.25057 10 0.25057 14 25 9 G.F. Nelson 1202 1118 559 0.93012 6 0.46506 1 0.50000 1 8 1 A.F. Paul 1199 995 279 0.82986 10 0.23269 12 0.28040 11 33 12 D.K. Raulson 597 496 233 0.83082 9 0.39028 4 0.46976 2 15 4 T.R. South 1702 1345 551 0.79025 12 0.32374 6 0.40967 6 24 8 E.A. Thomas 2422 2180 567 0.90008 7 0.23410 11 0.26009 12 30 11 C.F. Viney 1724 1293 388 0.75000 14 0.22506 13 0.30008 9 36 13 F.E. Yousef 980 804 209 0.82041 11 0.21327 14 0.25995 13 38 14 Totals 23067 20286 7118 0.87944 0.30854 0.35088 EWCC A.D. Blaise 905 688 275 0.76022 12 0.30387 9 0.39971 7 28 10 I.A. Frank 1667 1467 719 0.88002 5 0.43131 2 0.49012 1 8 2 S.D. Gundel 2374 1899 741 0.79992 11 0.31213 7 0.39021 8 26 9 P.O. Hogan 392 298 116 0.76020 13 0.29592 11 0.38926 9 33 12 W.M. Kraft 1998 1938 620 0.96997 1 0.31031 8 0.31992 12 21 7 L.I. Luebbers 1357 1194 490 0.87988 6 0.36109 5 0.41039 5 16 6 J.H. Nye 129 111 48 0.86047 7 0.37209 4 0.43243 4 15 4 J.A. O'Dell 953 896 287 0.94019 2 0.30115 10 0.32031 11 23 8 R.W. Pauly 2229 1962 785 0.88022 4 0.35218 6 0.40010 6 16 5 K.G. Ross 2808 2331 1049 0.83013 8 0.37358 3 0.45002 3 14 3 D.S. Smith 2812 2250 765 0.80014 10 0.27205 12 0.34000 10 32 11 J.P. Trost 1095 898 225 0.82009 9 0.20548 13 0.25056 13 35 13 M.M. Wall 1745 1571 754 0.90029 3 0.43209 1 0.47995 2 6 1 Totals 20464 17503 6874 0.85531 0.33591 0.39273 NWCC D.H. Allen 333 303 124 0.90991 6 0.37237 3 0.40924 6 15 3 T.G. Black 1422 1081 400 0.76020 12 0.28129 9 0.37003 7 28 11 M.A. Carter 360 310 90 0.86111 8 0.25000 13 0.29032 12 33 13 M.P. Drake 2636 2241 1053 0.85015 9 0.39947 2 0.46988 2 13 2 J.K. Elmsworth 739 554 244 0.74966 13 0.33018 6 0.44043 3 22 8 P.T. Grey 1848 1515 651 0.81981 10 0.35227 5 0.42970 4 19 5 C.R. Heines 1985 1826 548 0.91990 2 0.27607 10 0.30011 11 23 9 D.R. Jones 1417 1332 386 0.94001 1 0.27241 12 0.28979 13 26 10 B.M. Keith 2824 2570 848 0.91006 5 0.30028 7 0.32996 9 21 7 G.H. Matheson 1495 1375 688 0.91973 4 0.46020 1 0.50036 1 6 1 P.R. Neighbors 2652 2307 969 0.86991 7 0.36538 4 0.42003 5 16 4 S.T. Orion 1310 1205 374 0.91985 3 0.28550 8 0.31037 10 21 6 A.P. Tracey 1146 928 316 0.80977 11 0.27574 11 0.34052 8 30 12 Totals 20167 17547 6691 0.87008 0.33178 0.38132

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