Statistics is about more than calculations. It is about turning data into information and using this information to understand the population. A statistician will be asked to help solve real world problems by designing a study, collecting data, analyzing the data, and writing up the results. As a final project, you will be asked to do something similar. Though the design and data collection will be done for you, you will be asked to analyze the data using the appropriate tests (ensuring the data are distributed normally) and write up the results, using statistical evidence to support your findings. Lastly, you will be asked to include recommendations, that is, apply the results to solve the real world problem.
In your paper, explain why you chose each statistical test, figure, or procedure.
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 5-10 pages (including figures), explain your recommendations, using statistical evidence to support your findings. The data found are below:
|
Shoe Size
|
Height
|
Gender
|
Shoe to Height Ratio
|
|
Shoe Size
|
Height
|
Gender
|
Shoe to Height Ratio
|
|
7
|
64
|
Male
|
0.109375
|
|
5
|
63
|
Female
|
0.07936508
|
|
11
|
72
|
Male
|
0.15277778
|
|
7.5
|
70
|
Female
|
0.10714286
|
|
12
|
72
|
Male
|
0.16666667
|
|
9
|
70
|
Female
|
0.12857143
|
|
14
|
76
|
Male
|
0.18421053
|
|
7
|
66
|
Female
|
0.10606061
|
|
10.5
|
71
|
Male
|
0.14788732
|
|
7.5
|
71
|
Female
|
0.1056338
|
|
11
|
71
|
Male
|
0.15492958
|
|
8
|
68
|
Female
|
0.11764706
|
|
10
|
69
|
Male
|
0.14492754
|
|
6.5
|
65
|
Female
|
0.1
|
|
12
|
69
|
Male
|
0.17391304
|
|
7
|
67
|
Female
|
0.10447761
|
|
10.5
|
72
|
Male
|
0.14583333
|
|
7.5
|
70
|
Female
|
0.10714286
|
|
12
|
73
|
Male
|
0.16438356
|
|
6.5
|
65
|
Female
|
0.1
|
|
9.5
|
69
|
Male
|
0.13768116
|
|
6
|
60
|
Female
|
0.1
|
|
11.5
|
70
|
Male
|
0.16428571
|
|
6.5
|
64
|
Female
|
0.1015625
|
|
14
|
75
|
Male
|
0.18666667
|
|
10
|
72
|
Female
|
0.13888889
|
|
13.5
|
77
|
Male
|
0.17532468
|
|
6.5
|
63
|
Female
|
0.1031746
|
|
9.5
|
68
|
Male
|
0.13970588
|
|
7
|
68
|
Female
|
0.10294118
|
|
13
|
72
|
Male
|
0.00194036
|
|
6
|
62
|
Female
|
0.09677419
|
|
11
|
73
|
Male
|
0.15068493
|
|
7
|
66
|
Female
|
0.10606061
|
|
|
|
|
|
7.5
|
70
|
Female
|
0.10714286
|
If the Nyke Company feels that they only need to make one size of shoe regardless of gender or height, we would expect the shoe to height ration to be the same for both male and female.
H0: shoe to height ratio for male = shoe to height ratio for female
Two-sample T for shoe to height ratio
|
Gender
|
Total
|
Mean
|
Standard Deviation
|
SE Mean
|
|
Male
|
17
|
0.14712904
|
0.041972025
|
0.010179711
|
|
Female
|
18
|
0.10625479
|
0.012536011
|
0.002954766
|
Difference = mu (male) - mu (female)
Difference = 0.04087425
95% CI for difference is (0.04001, 0.06276)
T-Value= 9.19
P-Value=0.000
With a P value < 0.05 we can reject the null hypothesis.
Conclusion: Nyke needs to make different size shoes for both gender and height.