Statistical Analysis for Business Decision

[Name of the Author]

[Name of the Institute]

Table of Contents

Introduction1

Methodology1

Hypotheses1

Analyses2

Descriptive statistics2

Test of relationship3

Hypothesis4

Level of Significance4

Test of Hypothesis5

Decision5

Testing for difference between means6

Difference in shoe size between genders6

Difference in height between genders10

Recommendations14

References16

Introduction

This research study focuses on a business decision of a shoe company, Nyke. Nyke has been hit hard by a financial crisis and for cost reduction the company needs to find if they can minimize their product portfolio. The company is working on a new business model which implies that the company makes only one shoe size regardless of the height or gender of the customer. For this business model to be implemented, the company needs statistical evidence that supports the idea of make only one size of show. In this paper different statistical tools and techniques are used to analyze a sample provided by the company, in order to give statistically significant recommendation to the company regarding the new business model.

Methodology

The methodology of the statistical analysis consists of developing two hypotheses, one in favor of the new business model, and the other is in opposition to the new business model. Correlation is calculated to find if there exists a significant relationship between the heights of the customers and the shoe size that fits them. Furthermore, different tests of hypothesis are used to find if there exists difference between the genders in relation to their height and shoe size.

Hypotheses

Null hypothesis: The new business model, that constitutes the company to make only one shoe size regardless of the height and gender, can be implemented as evident by statistical analyses.

Alternate hypothesis: The new business model, that constitutes the company to make only one shoe size regardless of the height and gender, cannot be implemented as evident by statistical analysis.

Analyses

Descriptive statistics

Descriptive Statistics

Statistic

Bootstrapa

Bias

Std. Error

95% Confidence Interval

Lower

Upper

Shoe Size Female

N

17

0

0

17

17

Minimum

5

Maximum

10

Mean

7.09

.01

.28

6.59

7.68

Std. Deviation

1.162

-.052

.251

.609

1.585

Shoe Size Male

N

17

0

0

17

17

Minimum

7.00

Maximum

14.00

Mean

11.2941

.0140

.4363

10.4706

12.1471

Std. Deviation

1.80329

-.08371

.31793

1.11063

2.33222

Valid N (listwise)

N

17

0

0

17

17

a. Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples

The descriptive statistics show that mean shoe size for females is 7.09, with a 95% confidence interval of 6.59 to 7.68. And the mean shoe size for males is 11.29, with a confidence interval of 10.47 to 12.14. These intervals were obtained after running bootstrap on the samples.

Test of relationship

The research question is to find whether a single shoe size compatible to majority of the customers regardless of the gender and height can be made or not. Answer of this highly depends on the relationship, if any, that exists between the shoe size and heights. The correlation between heights and shoe sizes of the subjects involved in the sample is tested. The table below shoes the computation of the correlation

 

Show Size

Height

Show Size

1

Height

0.864340313

1

The correlation between shoe size and heights of the subjects turned out to be 0.864. This number indicates that between shoe size and heights, there exists a strong positive relationship. The positive relationship means that the direction of the movement of both the variables is same and the state of this positive relationship is very strong. The direction of the movement of variable implies that if “Height” goes up the ...