This assignment is designed to provide you with hands-on experience in generating random values and performing statistical analysis on those values.

Overview and Rationale

This assignment is designed to provide you with hands-on experience in generating random values and performing statistical analysis on those values.

 Course Outcomes

This assignment is directly linked to the following key learning outcomes from the course syllabus:

·  Use descriptive, Heuristic and prescriptive analysis to drive business strategies and actions

Assignment Summary 

Follow the instructions in this project document to generate a number of different random values using random number generation algorithm in Excel, the Inverse Transform. Then apply the Chi-squared Goodness of Fit test to verify whether their generated values belong to a particular probability distribution. Finally, complete a report summarizing the results in your Excel workbook. Submit both the report and the Excel workbook.

 The Excel workbook contains all statistical work. The report should explain the experiments and their respective conclusions, and additional information as indicated in each problem. Be sure to include all your findings along with important statistical issues.

Format & Guidelines

The report should follow the following format:

 (i)       Introduction

ii)       Analysis

(iii)      Conclusion

And be 1000 - 1200 words in length and presented in the APA format

Project Instructions: 

The project consists of 4 problems and a summary set of questions. For each problem, tom hints and theoretical background is provided.

 Complete each section in a separate worksheet of the same workbook (Excel file). Name your Excel workbook as follows:

 ALY6050-Module 1 Project – Your Last Name – First Initial.xlsx

 In the following set of problems, r is the standard uniform random value (a continuous random value between 0 and 1).

 Problem 1

Generate 1000 random values r. For each r generated, calculate the random value X by:

𝗑 = −𝐿𝑛(𝑟),

where “Ln“ is the natural logarithm function.

Investigate the probability distribution of X by doing the following:

 1.      Create a relative frequency histogram of X.

2.      Select a probability distribution that, in your judgement, is the best fit for X.

3.      Support your assertion above by creating a probability plot for X.

4.      Support your assertion above by performing a Chi-squared test of best fit with a 0.05 level of significance.

5.      In the word document, describe your methodologies and conclusions.

6.      In the word document, explain what you have learned from this experiment.

 Hints and Theoretical Background

 A popular method for generating random values according to a certain probability distribution is to use the inverse transform method. In this method, the cumulative function of the distribution (F(x)) is used for such a random number generation. More specifically, a standard uniform random value r is generated first. Most software environments are capable of generating such a value. In Excel and R, functions “=RAND()” and “runif()” generate such a value respectively. After r has been created, it  then replaces F(x) in the expression of the cumulative function and the resulting equation is solved for the variable x.