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 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 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. Gender and shoe size will be the only criteria used in selecting a shoe for Nyke Shoe Company. Originally, we determined that the mean of all shoes worn by our 35 participants (male and females included) was nine and we could very easily attempt to select it for the company. However, if we were to look at the shoe sizes amongst all participants, only one participant actually wears a size 9, therefore, it makes more sense to reject that idea.
Another approach can be taken by breaking down the data into two separate sets (females and males). It seems as though the best shoe size option for both females and males are 7 and 11 based on the values of the mean, median, and mode. We could select 6.5 or 7.5 for females, but chances are that some females might choose a slightly larger size than 6.5 or slightly smaller than a 7.5. On the other hand, males have a fewer options compared to the female shoe sizes because there were only two participants wear size 10.5 or below 11 and only one size 11 or above. There is not much sense in wasting money to produce size 11. Therefore, production of shoes for males will be rejected and the focus will be only on shoes for females. In comparison to any other size for all participants, female shoes of size 7 have a better multiplicity above and below. Conclusion
The safest bet in order for the Nyke Company to come out of a possible bankruptcy situation is to focus only on female shoes of size 7. The result will remain consistent if the prices are the same for all shoes irrespective of gender and shoe size. If there are more data numbers and/or the pricing is not the same across-the-board, then a new study will have to be undertaken to reflect the new factors.