The Problem Due to financial hardship, the Nyke Shoe Company feels they only nee

Question

The Problem

Due to financial hardship, the Nyke Shoe Company feels they only need to make one size of shoes, regardless of gender or height. They have collected data on gender, shoe size, and height and have asked you to tell them if they can change their business model to include only one size of shoes—regardless of height or gender of the wearer. In no more than 5–10 pages (including figures), explain your recommendations, using statistical evidence to support your findings. The data found are given in the following table.

Only use results in the paper. You may show your work in an appendix, if you would like.

Shoe Size    Height Gender 5 63 Female 7.5 70 Female 9 70 Female 7 64 Male 11 72 Male 12 72 Male 14 76 Male 7 66 Female 7.5 71 Female 8 68 Female 10.5 71 Male 11 71 Male 6.5 65 Female 7 67 Female 7.5 70 Female 10 69 Male 12 69 Male 6.5 65 Female 10.5 72 Male 12 73 Male 6 60 Female 6.5 64 Female 10 72 Female 9.5 69 Male 11.5 70 Male 14 75 Male 6.5 63 Female 13.5 77 Male 7 68 Female 9.5 68 Male 13 72 Male 11 73 Male 6 62 Female 7 66 Female 7.50    70 Female

Explanation / Answer

According to the given data on shoe size,height,and gender,if the company wants to make only one size shoe,then that must be depends on the modal value of the shoe size,i.e the value of the shoe size which repeat maximum number of times.

TOTAL 35

Here shoe size 7 occure maximum number of time.So mode of the data is(shoe size ) 7.Therefore if the company ignore gender and height,then only product 7th size shoe.

Now we are checking whether it is correct to ignore the gender on the shoe size or no.

Shoe

Size   

Here ,according to the gender (female) the mode of the shoe size is 6.5,7, and 7.5

And according to the Male record,

Shoe

Size   

the mode of the shoe size is 11,12.

So ,we can see that shoe size depends on gender.The shoe size of the female is relatively small than the Male shoe size.So we can not ignore the gender while choosing the shoe size.

Now we are checking whether show size depends on height or not.

Shoe

Size   

Here we can see that the shoe size more or less increase with the increase of height. And if we consider the correlation between the shoe size and height ,it is 0.875682 ,which is quite high,and shows a positive correlation.

So while deciding the shoe size we can not even ignore the height of the person.

So the company should produce the shoes according to the modal value depending on the gender ,separately,i.e produce shoe size 6.5,7, and 7.5 for female and 11,12 for males and accornding to the height ,produce size 7 for both the gender in its financial crisis time.

So according to the statistics,they should not change their business model to include only one size of shoes—regardless of height or gender of the wearer.

shoe size frequency 5 1 6 2 6.5 4 7 5 7.5 4 8 1 9 1 9.5 2 10 2 10.5 2 11 3 11.5 1 12 3 13 1 13.5 1 14 2

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