# Senior Theses

2005

Anne Louise Humphrey
"
Expected Value of Sample Information
"

The purpose of this project is to explore and make observation on expected value of sample information (EVSI). In general, this is a large topic so I looked at a particular example where I had two weighted coins, coin X and coin Y, where the probability of getting heads with coin X is and the probability of getting heads with coin Y is . I started off looking at cases where and have a discrete prior probability distribution and then moved on to cases where and have a continuous prior probability distribution, namely the beta distribution, which was used because it is the conjugate prior for the binomial distribution.

Amanda King
"
Survey of Statistical Background and Habits of California Secondary Mathematics Teachers
"
Advisor: Beth Chance and Allan Rossman (bchance@calpoly.edu, arossman@calpoly.edu)

Statistics at the high school level is a relatively new development and little is known about the learning and teaching environment of Statistics at the high school level. The purpose of this research study was to gain information about the high schools that offer Statistics, the methods being used to teach Statistics and the preparation of teachers teaching Statistics at the high school level.

Nick Magill
"
Is There a Better Way to Play the World Series?
"

The goal of this project was to determine if there is a better set up for the World Series other than a best-of seven. The analysis was based on the typical best-of series as well as a new one. The second series analyzed was one in which a team wins as soon as it is ahead by two games. In order to determine which series was better, two measures were taken and a third was created. The best series was determined to be one which has a high probability of choosing the better team as the winner and doing so in a minimum number of games. A loss function was then created to measure the utility of each type of series. In doing this analysis some interesting results were found. I found that if there is a large gain associated with choosing the better team as the winner then for the most part, the classic best of series is the best. When there is less gain associated with choosing the better team as the winner, then the new win by two series can be found to have the most utility.

Aaron Quan
"
Parity and Competitive Balance in Professional Sports
"

Many have suggested that there is more parity or competitive balance in the National Football League (NFL) recently. In this report I analyzed the trends in parity over time, starting in 1966, in three professional sports: NFL, MLB, and NBA. I define various measures of parity and then analyze how the parity measures have changed over the past forty years in each sport. I also simulated NFL seasons under a model of perfect parity to determine the distribution of certain measures of parity. I also considered how much a team's record fluctuates from one season to the next as another measure of parity. Finally, I compare a sport's parity measures before and after the advent of free agency in each sport to see if there is a significant difference in the level of competitive balance.

2003

Colleen Kreutner
"
Investigating Extensions of the Secretary Problem
"