Barbara Greczyn

STA 201 - Principles of Statistics

Instructor Alok Dihtal

April 26, 2015

Introduction Nyke Shoe Company has been in business for over 50 years. Over the last five years, the company has been undergoing some financial hardship due to an erratic market and an inability to understand what the consumer actually needs. In a last ditch effort to avoid bankruptcy, they have adopted a new business model which entails the development of only one shoe size. In order to achieve this goal, statistical data must be utilized and applied to make the best choice. The data used will be explained to the fullest and a conclusion will be then obtained.

Methodology

A sample group of 35 participants was gathered, 18 females and 17 males. Their heights and shoe sizes were gathered and their data was processed in three categories: shoe size, height, gender. Descriptive statistics was applied to three separate data sets, one with all participants included, one sets with just female participants, and one with just male participants. Then a two sample t-test was conducted with the assumption that there were unequal variances amongst both male and female data sets.

Results

There is a normal distribution of the data with ranges in size from size 5 to size 14 amongst the participants. With these ranges, the mean is 9.142, with a standard deviation of 2.583 and a variance of 6.670. Appendix B: Male vs. Female data sets, show the mean, standard deviation and variance for both of these sets respectively. Female data sets have a mean of 7.111, standard deviation of 1.131, and a variance of 1.281 whereas the males have a mean of 11.294, a standard deviation of 1.803, and a variance of 3.251. The T-test was applied to these two data sets to obtain a result of (2-tailed): 1.4964E-09. Since both of the data sets (females and males) each have less than 30 samples, the t-Test was chosen. Assuming equal