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下面为大家整理一篇优秀的Report范文- The price difference between high heels and non-high heels，供大家参考学习，这篇论文讨论了高跟鞋和非高跟鞋的价格差异。我们经常看到女性会在时尚杂志或者时装表演穿高跟鞋，由于这些情况常常与荣耀、财富联系在一起，所以高跟鞋会显得比较昂贵。而经过调查，高跟鞋的价格也确实要比非高跟鞋贵得多。这可能意味着高跟鞋是时尚的象征，购买它的人会显得更有购买力。

Introduction

We often see that woman wear high heels in fashion magazines, fashion shows and important events. Since those situations are also often associated with wealth and glory, I wonder whether the price of high heels is significantly higher than the price of non-high heels. This paper consisted of a random selection of 20 high heels and 20 non high heels from malls of different styles and brands. Then I will perform the hypothesis test and calculate the confidence interval.

Data Gathering

I went to department stores such as Macy’s and Dillard’s as well as brand stores such as Forever 21, H&M, Clarks and etc. to randomly collect the price of high heels are non-high heels. Since the shoes are all on a shelf, I started to count from the upper left corner and took the price of the first high heel and the price of the first non-high heel. I took at most 10% of all the shoes that they sell. For example, Clarks has many shoes on display but Forever 21 only have about 10 different styles, then I only took one sample from Forever 21. For those stores with a large number of shoes on display, I also took approximately 10% of those shoes as a sample. I took the 1st, 5th, 10th, shoes on the shelf and so on. I went to 7 different stores to get my data to make sure that it is a random selection and that the sample can be representative of all the high heels and non-high heels in America. The prices will be rounded to an integer for convenience and the unit is in dollars.

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The Data

Data Summary

Stem and leaf for high heels

From the stem and leaf plot, we can conclude that the data is skewed to the right. The mean is greater than the median. The data is symmetric, unimodal and does not have outliers.

Stem and leaf for non-high heels

The stem and leaf tells us that the data is a little skewed to the right, approximately normally distribution, symmetric, unimodal with no outliers.

Back to back stem and leaf plot

Inference

Conditions for conducting a hypothesis test

Although both categories of my data are a little bit skewed to the right, they are still normally distributed and meet the conditions for performing a hypothesis test. The sample that I gathered is independent, and the two groups are also independent. Both of the groups are approximately normally distributed and the sample is smaller than 10% of the population of all shoes sold in America.

Hypothesis test

My null hypothesis is that the price for high heels is not significantly higher than the price for non-high heels. The alternative hypothesis is that the price for high heels is significantly higher than the price of non-high heels. I used the unmatched (independent) two –sample t test.

t= ((ave.x1-ave.x2)-(µ1-µ2))/√(〖s1〗^2/n1+〖s2〗^2/n2)=((101.5-59.45))/√(40.501/20+40.958/20)

Using this equation and excel, the t test is 3.2646.

DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }

= (40.5012/20 + 40.9582/20)2 / { [ (40.5012 / 20)2 / (20 - 1) ] + [ (50.9582 / 20)2 / (20 - 1) ] }=38

With 38degrees of freedom, the critical value for a 95% confidence level is 1.66. I am using the 95% because this is a one sided test. Since 3.2646>1.684, I can reject the null hypothesis and conclude that the price of high heels is significantly higher than the price of non-high heels. The p value is 0.0012, which is smaller than 5%. This also signifies that we can reject the null.

Confidence interval

Upper limit =(ave.x1-ave.x2)+t*SD of difference in means

= (101.5-59.45)+1.684*12.8802

Lower limit=(ave.x1-ave.x2)-t*SD of difference in means

= (101.5-59.45)-1.684*12.8802

So the confidence interval is (20.359, 63.74)

Since 0 is not in the confidence interval, I can reject the null hypothesis and conclude that the price of high heels is significantly higher than the price of non-high heels.

Conclusion

In conclusion, I learned that high heels are priced significantly higher than non-high heels.This may mean that high heels are a symbol of fashion and are more likely to be purchased by people with a higher purchasing power.

If I were to do this project again, I can be more specific into exactly how high the high heel is and conduct a project on whether the height of high heels has any influence in how the high heel is priced. For example, I can separate the high heels into “heels lower than 2 inches” category and the “heels higher than 2 inches” category.

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