Final Project: Nyke Shoe Company
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
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The null hypothesis was that the female and male shoe sizes have an equal mean while the alternative hypothesis was that female and male shoe sizes do not have an equal mean. With the degrees of freedom being 33, the t-statistic is -8.27. The probability that -8.27 is ≤-1.69 is 7.5×10-10 for the one-tailed test. Also, the probability that -8.27 is ≤ ±2.03. is 1.5×10-9 for the two-tailed test. Due to both probabilities being under the alpha value of 0.05, the null hypothesis is rejected, and the alternative hypothesis is accepted at the 95% confidence level.
Assuming unequal variances, the two sampled t-Test was applied on the data sets of female and male shoe sizes with the alpha value of 0.05. The null hypothesis was that the female and male shoe sizes have an equal mean while the alternative hypothesis was that female and male shoe sizes do not have an equal mean. With the degrees of freedom being 27, the t-statistic is -8.16. The probability that -8.16 is ≤ -1.70 is 4.5×10-9 for the one-tailed test. Also, the probability that -8.16 is ≤ ±2.05. is 9.1×10-9 for the two-tailed test. Given that both probabilities are under the alpha value of 0.05, the null hypothesis is therefore rejected, and the alternative hypothesis is accepted at the 95% confidence level.
Discussion
After a close look at the data sets, it has been determined that there is no correlation between height and shoe size, therefore, the height will be ignored in selecting a shoe.
According to above analysis, we have found that there is a strong positive correlation between the shoe sizes and heights.
(1) A study of the number of cars sold looked at the number of cars sold at 500
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