Reference no: EM13620451

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.