Question:

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 5-10 pages (including figures), explain your recommendations, using statistical evidence to support your findings. The data found are below:

Shoe Size| Height| Gender|
5.00| 63.00| Female|
7.50| 70.00| Female|
9.00| 70.00| Female|
7.00| 64.00| Male|
11.00| 72.00| Male|
12.00| 72.00| Male|
14.00| 76.00| Male|
7.00| 66.00| Female|
7.50| 71.00| Female|
8.00| 68.00| Female|
10.50| 71.00| Male|
11.00| 71.00| Male|
6.50| 65.00| Female|
7.00| 67.00| Female|
7.50| 70.00| Female|
10.00| 69.00| Male|
12.00| 69.00| Male|
6.50| 65.00| Female|
10.50| 72.00| Male|
12.00| 73.00| Male|
6.00| 60.00| Female|
6.50| 64.00| Female|
10.00| 72.00| Female|
9.50| 69.00| Male|
11.50| 70.00| Male|
14.00| 75.00| Male|
6.50| 63.00| Female|
13.50| 77.00| Male|
7.00| 68.00| Female|
9.50| 68.00| Male|
13.00| 72.00| Male|
11.00| 73.00| Male|
6.00| 62.00| Female|
7.00| 66.00| Female|
7.50| 70.00| Female|

To start out, let’s examine if there is a correlation between the shoe size and the height. Using Excel, we obtain the following table (see sheet CORRELATION)

| Shoe size| Height|
Shoe size| 1| |
Height| 0.86434| 1|

As we can see that the correlation coefficient R=0.86434 is positive and close to 1, it suggests that there is a strong positive relationship between the shoe size and the height.

Next, let’s formulate the following data (see SHOW SIZE DATA)

Using Excel to get the following descriptive statistics for both variables: shoe sizes for females (FEMALE) and shoe sizes for males