STAT 3203 Statistics for Accounting and Business

Final Project – 10%

The purpose of this assignment is to provide the student an opportunity to apply the course concepts in a real life situation and in the process, develop analytical and practical skills.  A data set has been selected and posted on Canvas in an Excel file titled “FinalProjectDataFirmSize.xls”.  Download this file so you can use and analyze the information for the final project.

The data are from the US Small Business Administration yearly report from 2007.  The first column shows ranges of firm size for the different categories (firm size refers to the number of people employed by a given firm).  For each firm size range, you will find the number of firms that fit within that range as well as the total number of people employed in that range.  For example, in the 5-9 employees range, there are a total of 1,060,250 firms and 6,974,591 employees divided among those firms.  Column E has the total amount spend on payroll for all firms in the category.  So for the firms with 5-9 employees, a total of $222,419,546,000 is spent across the over 1 million firms (remember the number shown in the column is in thousands of dollars).  Column G shows the total annual amount of money received into the firms in the category.  Continuing with our example, the 1 mil+ firms in the 5-9 employee category received a total of $1,144,930,232,000 when you add up the receipts of each of the firms in the category.

Three columns of useful information are missing, so you must fill in the information.  First, you must find the midpoint of the firm size range shown in Column A.  Do this by finding the average between the minimum and maximum of the range.  For the final category (5,000 and up), use 20,000 as the midpoint.   Second, you will need to find the mean payroll per employee for each firm size category.  Column E is the total amount paid to all employees and column D is the total number of employees.    Remember, column E is in 1,000s of dollars so in order to find the mean payroll in dollars (not 1000s of dollars), you must multiply your answer by 1,000.  Thirdly, you must find the mean annual receipts per firm for the firms in the category.  Column G gives the total annual receipts for all firms in the category in $1000s and column C gives the number of firms in the category.  You can make any additional calculations that you find useful using the data given.  If you choose to do so, explain how and why you make each calculation.

Parts of this project can be completed earlier in the course as the topics are covered.  Doing the part that relates to the current material as it is covered will help you keep the project on track instead of having a large volume of work to do at the very end.

A successful report should contain the following elements:

1. Visual representations of the data.  You may choose which of the chart types covered in the class to use.  You may choose to do it all in one chart or use multiple charts.  Be sure to label your charts well.  If you would like to use a different type of chart, you must first have it approved by the professor.
2. Determine the correlation between each of the pertinent data labels and justify why this correlation should be calculated and interpret the correlation you found.  You can show correlation visually as well, but you must include the numerical calculations.  Since Column F (Mean Pay Per Employee) is calculated from Column D (Total Employment) and Column E (Total Annual Payroll), you should not find the correlation between Columns F and D or E.  Likewise, the correlation between Columns A and B would not be useful information as well as finding the correlation between column H and either column C or G.
3. Find an equation for the regression line for the pairs of variables that have a significant relationship from part 2.  You must do at least 1 regression line and may choose to do more.  Interpret your results.  Be careful when determining which variable is the dependent one and include a justification for your choice.  You may choose to include a visual representation of the data along with the regression line found.
4. Use the regression line(s) found in 3 to predict values not included in your independent variable sample but that are within the predictive range of the data.  Interpret these values.  You must have at least 1 prediction for each regression line.
5. Find a multiple regression equation.  Choose the mean receipts per firm in category (column H) as the dependent (or y) variable and choose the midpoint of firm size (column B) and the mean pay per employee (column F) as the independent (or x) variables.  Interpret your results.
6. Perform a hypothesis test for at least one of the regressions you chose to include in the paper.  Be sure to include both the null and the alternative hypothesis, the test being performed and why, the relative test statistic, and the conclusion you can draw from the test.
7. At least one Bible reference that pertains to the subject as well as 2 quality reference articles.  The Biblical reference does not have to be a specific verse or passage per say, but include how the topic relates to Biblical principles and ideals.  You can relate the Biblical content to statistics in general or to the topic of wages.
8. Include a cover sheet and reference page using APA standards.

The components outlined above will be integrated into a comprehensive final report paper.   This report should be APA formatted, a minimum of 5 pages in length, exclusive of appendices, table of contents, references, and cover sheet. The report must contain at least 2 quality reference articles - these must be appropriately cited and placed in a references page per APA requirements.

This paper will be graded based on the analysis and summary, as well as the overall clarity and effectiveness of the work.   See page 22 of the syllabus for a grading rubric.