## Mathematics, Engineering and Computer Science Undergraduate Theses

Spring 2009

Thesis

#### Department

Mathematics, Engineering & Computer Science

Kelly Cline

Philip Rose

Charlotte Jones

#### Abstract

A statistical analysis of the effects of arrow diameter on score was done in order to determine if having a larger arrow diameter would help to increase one’s score. To gather the data four different skill levels of archers were found and they shot two different arrow diameters, one ideal and one that was one size larger. Once all the data was gathered I used the Central Limit Theorem to conclude that the mean of my data, x, was normal distributed. Considering the mean of my data was normally distributed, all of the methods described below were able to be used to complete the statistical analysis. A table of the descriptive statistics can be found in Appendix B. With all of the descriptive statistics completed a null hypothesis and an alternative hypothesis were needed in order to complete the hypothesis tests. //0:(//,- /Z2 ) = 0 and Ha: /ix> /z2 were used as the parameters for the hypothesis test, with an alpha of 0.05. //, was the average score of the ideal arrow diameter, whereas /z2 was the average score of the larger diameter arrow. Using these parameters the null hypothesis was rejected for the beginning archer, with a p-value of 0.00903. Yet, the null hypothesis was unable to be rejected for the other three categories of archers. Once the hypothesis tests were completed, an analysis of variance, or ANOVA, was conducted. This analysis gave a p-value of 0.00294. Therefore, the null hypothesis was rejected, stating that arrow diameter may affect score. It was determined that arrow diameter does seem to affect score, but it does not appear to improve an archer’s score.

COinS