Capstones in Statistics

2003

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SET and All Its Glory
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By altering the original deck of cards for the game SET®, an investigation into the mathematics of the new deck evolves.  The cards in the new deck still have four attributes, but now the attributes vary in number of values.  The investigation includes the number of cards in the deck, the number of sets given a premise at different times and the cap for the game.  The game can be played by finding sets of three cards or sets of four cards.  Since the new deck has attributes that vary in number, different combinations for each set must also be considered.

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Markov Chains and the SORRY! Board Game
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Investigations into board games using Markov Chains have been used in the past to provide information and strategies on how to win.  Here the game SORRY! was the subject of investigation, this time focusing on the expected number of moves needed to be taken in order to move from the START position to HOME.  Due to the restrictions of the game, a “one-player” scenario was created to allow Markov Chains to be properly applied to the situation.  Each card was analyzed to determine the probability of movement from one space to another and these probabilities were placed into a 60X60 matrix.  With all other probabilities of movement fixed, the probability of movement using the 10 card was varied in order to determine the minimal number of turns needed to complete the “one” player game.

Joshua Caplinger
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Activity Networks
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Activity networks are directed graphs used to coordinate a set of activities in some type of project.  A path is defined to be a group of activities that establish a connection between the start and finish nodes.  The critical path of an activity network is the most important path because a delay in any one of these activities will cause a delay in the overall project. In this study, each activity in a constructed activity network was given is the form of a triangular distribution.  The expected values and the variances of each activity were calculated in order to determine which of the paths was the critical path.  It was observed, using Tchebysheff’s theorem, that each path could possibly be a critical path. Presented at the MAA regional Conference in DuBois, Pennsylvania, April 4.

Kevin Culp
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Strategy for NCAA College Football Overtime Games
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Results from past NCAA division IA seasons are analyzed and hypothesis testing and regression analysis techniques are used to determine which independent variables are most important to success and which factors of overtime games contribute most to a team’s success.  A strategy is determined and tested using other overtime games from past years in NCAA division IAA. Presented at the MAA regional Conference in DuBois, Pennsylvania, April 4.

2001

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Seeding Teams in the Men's 2001 NCAA Basketball Tournament
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Two seeding methods for the NCAA tournament were examined, traditional, in which the best team faces the worst in in first round play and cohort randomized method in which several teams are grouped and then randomly assigned to play against each other.  The mathematics behind the seeding methods were examined.  Application of both methods were applied in a simulation of the tournament using Las Vegas odds. Presented at the MAA regional conference in Altoona, April 6.

Amy Vaccari
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Routing of School Buses by Computer
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