# Statistics Final

10 October 2016

For females was 7. 11 with a standard deviation of 1. 13 For males was 11. 29 with a standard deviation of 3. 25. It seems that there is a significant difference between the average shoe sizes for females and for males. To find out a more correct answer, letβs conduct an independent sample t-test in the following. Denote by the average shoe sizes for males and females, respectively. Here are the two hypotheses: Null hypothesis H0: Alternative hypothesis Ha: We conduct an independent sample t-test using Excel, and obtain the following output (see sheet T-TEST) -Test: Two-Sample Assuming Unequal Variances| | | | | shoe size(female)| shoe size (male)| Mean| 7. 111111111| 11. 29411765| Variance| 1. 281045752| 3. 251838235| Observations| 18| 17| Hypothesized Mean Difference| 0| Β | df| 27| Β | t Stat| -8. 165111165| Β | P(T&lt;=t) one-tail| 4. 52926E-09| Β | t Critical one-tail| 1. 703288423| Β | P(T&lt;=t) two-tail| 9. 05852E-09| Β | t Critical two-tail| 2. 051830493| Β | From the above output, we can see that the p-value is 9. 05852E-09, which is smaller than 0. 05 (if we select a 0. 05 significance level). So, we should reject the null hypothesis H0. At a 0. 5 level of significance level, we conclude that there is a significant difference between the average shoe size for females and the average shoe size for the males. We can also test if there is a significant difference between the average height for females and the average height for the males. Denote by the average heights for males and females, respectively. Here are the two hypotheses: Null hypothesis H0: Alternative hypothesis Ha: We conduct an independent sample t-test using Excel, and obtain the following output (see t-test-height) t-Test: Two-Sample Assuming Unequal Variances| | | | | height (F)| height(M)| Mean| 66. 66666667| 71. 5294118| Variance| 11. 88235294| 9. 867647059| Observations| 18| 17| Hypothesized Mean Difference| 0| | df| 33| | t Stat| -4. 207413941| | P(T&lt;=t) one-tail| 9. 30285E-05| | t Critical one-tail| 1. 692360258| | P(T&lt;=t) two-tail| 0. 000186057| | t Critical two-tail| 2. 034515287| | From the above output, we can see that the p-value is 0. 000186, which is smaller than 0. 05 (if we select a 0. 05 significance level). So, we should reject the null hypothesis H0. At a 0. 05 level of significance level, we conclude that there is a significant difference between the average height for females and the average height for the males.

Conclusion: According to above analysis, we have found that there is a strong positive correlation between the shoe sizes and heights. We also found that there is a significant difference between the average shoe size for males and the average shoe size for the females, and there is a significant difference between the average height for females and the average height for the males. So, it would not be good if they would change their business model to include only one size of shoes β regardless of height or gender of the wearer. Some other information to review:

The Size Difference * According to the Brannock Device, the most common sizing device, in the United States men’s shoe sizes are one size larger than women’s. That is to say, if a man wears a size 9, it is a size 10 in women’s shoes. Other Differences * Aside from the most obvious difference in length, women’s shoes are also made narrower than men’s shoes. This is because men’s feet are wider than women’s, because women generally have higher arches than men. Read more: The Difference Between Men’s and Women’s Shoe Sizes in the United States | eHow. om http://www. ehow. com/about_6553389_difference-shoe-sizes-united-states. html#ixzz2I3g2pyrS By allowing Nyke shoe factory to change their business model to only manufacturing ONE shoe size, regardless of height or gender can be a catastrophic financial problem for their business, which could lead and result into a total loss and shut down of the company. I would STRONGLY DISAGREE to allow the NYKE SHOE COMPANY to change their model from what they have now to only allowing one sized shoe to be manufactured. ——————————————–

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