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Research Experience at James Madison University

Hello everyone.  My name is Christopher Tait and I am a senior here at Hampden-Sydney.  I am a Mathematics, Applied Mathematics, and Mathematical Economics major.  I attended a Research Experience for Undergraduates(REU) at James Madison University this summer.  Dr. Pendergrass asked me to blog about my experience researching at JMU this summer. 

The REU included eight students with a total of four projects.  We were put into groups of two, each with a mentor.  I had the privilege of working with Dr. Nashimoto and my partner on problems with the binomial distribution.  Basically, we split the project into two parts.  The first part consisted of studying one-sample confidence intervals.  We looked at a variety of different intervals and tried to improve the overall coverage on the interval.  This coverage is difficult to obtain because of the erratic nature of the discrete binomial distribution. 

The second part of the project was enjoyable.  We studied simultaneous confidence intervals and attempted to improve the existing method’s Type I error.  First, we compared three new existing methods.  Then, we decided that it would be best to use a two-stage test in order to improve the Type I error.   The first stage of this two-staged test stayed consistent while we attempted different test statistics for the second stage.  We found that the least squares difference type test statistics worked the best.

Throughout the research, I learned new programs, which I believe will be very helpful to me as I start my senior year.  Two of the main programs I learned are R, which a free coding program offered by Microsoft, and LaTex.  LaTex is used by many professionals to write articles that are to be submitted to journals.  In doing the research this summer, I realized that I would like to pursue my PhD in Statistics.  I found the research to be extremely beneficial to my development as a mathematician and statistician. 

Concluding the research, my partner and I had to give a twenty minute presentation on what we found throughout the summer.  This part was the most difficult for me because I had to try to explain what we had done all summer through easily understandable terms to anyone who came to the talk.

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