Statistics Final Assignment

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Final Project

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The purpose of this assignment is to provide an opportunity to apply the concepts in a real life situation and in the process, develop analytic and practical skills. The data for this project is available here: FinalProjectDataFirmSize.xlsx

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 average annual wages for an employee of that firm size. So for the firms with 5-9 employees, on average, an employee earns $31,889.98 annually in wages. Column F shows the amount of revenue received by the firms in the given size. Continuing with our example, in the 5-9 employee category each firm made on average $1,079,870. Column G shows the revenues a company makes per employee they have. For the firms with 5-9 employees, each employee brought in about $164,157.33 in revenue for the firm. Column H shows the total amount a firm spent on wages to employees. For a firm with 5-9 employees, the firm would spend a total of $63,401.86 per year on wages to employees.

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. 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:

  • Visual representations of the data. You may choose which of the chart types covered in the class to use (Scatter, histogram, pie chart, etc). 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 from one presented in class, you should first have it approved by the instructor.
  • 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.
  • Find an equation for the regression line for the pairs of variables that have a significant relationship from part 2. You must calculate at least 1 regression line but 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.
  • 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.
  • Perform a hypothesis test for the correlation between two of the variables in 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. See page 478 in the textbook for step by step directions.
  • 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. The outside references should be from reliable sources who have looked into the relationship between your chosen variables of interest. For example, if you chose to focus on the impact of firm size on one of the other variables, you might look for articles on how the size of a company impacts that other variable.

The components outlined above will be integrated into a comprehensive final report paper, similar to a case study but with more information. This report should be APA formatted, a minimum of 5 pages in length, exclusive of appendices, table of contents, references, and cover sheet.

This paper will be graded based on the analysis and summary, as well as the overall clarity and effectiveness of the work. See page 19 of the syllabus for a grading rubric.

Rubric

Final Project Rubric

Final Project Rubric

Criteria Ratings Pts

This criterion is linked to a Learning Outcome Content: Identification and evaluation of issues

70.0 pts

Exemplary: You demonstrate clear critical thinking of the case and correctly apply principles in your solutions.

63.0 pts

Accomplished: You demonstrate a competent level of critical thinking of the case and correctly apply principles in your solutions.

55.0 pts

Developing: You demonstrate a limited amount of critical thinking of the case and apply some principles in your solutions

45.0 pts

Beginning: You demonstrate little to no critical thinking of the case and fail to apply principles in your solutions

70.0 pts

This criterion is linked to a Learning Outcome Ethical / Biblical principles – Recognition of appropriate application of ethical / biblical principles

10.0 pts

Exemplary: Well integrated and relevant to the issues identified

7.0 pts

Accomplished: Strong attempt at integration and relevance

5.0 pts

Developing: Limited applicability / relevance

3.0 pts

Beginning: Little to no integrating / relevance

10.0 pts

This criterion is linked to a Learning Outcome Structure & mechanics – Grammar and spelling, length, APA

20.0 pts

Exemplary: No grammar or spelling errors. All citations are correct. Length matches the required pages.

16.0 pts

Accomplished: Only a few grammar or spelling errors. Citations are correct. Length is less than the required pages.

13.0 pts

Developing: 3-5 spelling or grammar errors. Some citation errors. Length is less than the required pages.

9.0 pts

Beginning: More than 5 spelling or grammar errors. Multiple citation errors. Length is < required pages.

20.0 pts

Total Points: 100.0

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Unformatted Attachment Preview

Employer Firms, Employment, and Annual Payroll Small Firm Size Classes, 2007 Employment Size Midpoint of Firm Number of Firms in Total Employment in of Firm Size Range Category Category 0-4 3.705.275 6.139.463 5-9 1.060.250 6.974.591 10-14 425.914 4.981.758 15-19 218.928 3.674.424 20-24 134.254 2.928.296 25-29 89.643 2.405.637 30-34 64.753 2.063.987 35-39 47.641 1.754.582 40-44 38.221 1.600.913 45-49 29.705 1.391.754 50-74 86.364 5.195.105 75-99 41.810 3.582.686 100-149 39.316 4.749.055 150-199 18.620 3.205.201 200-299 17.780 4.309.143 300-399 8.155 2.808.347 400-499 4.715 2.101.982 500-749 6.094 3.695.682 750-999 2.970 2.561.972 1,000-1,499 2.916 3.552.259 1,500-1,999 1.542 2.664.416 2,000-2,499 942 2.094.728 2,500-4,999 1.920 6.687.266 5,000+ 1.927 39.481.018 Wages per Employee (in dollars) $ 38.264,15 $ 31.889,98 $ 33.354,20 $ 34.270,87 $ 34.688,99 $ 35.580,34 $ 35.716,09 $ 36.528,71 $ 36.850,13 $ 37.455,23 $ 37.460,92 $ 38.470,48 $ 38.838,28 $ 39.782,60 $ 40.127,68 $ 40.918,95 $ 41.425,26 $ 41.145,05 $ 42.870,60 $ 43.340,87 $ 45.265,62 $ 44.875,25 $ 47.947,90 $ 47.385,86 *Source: U.S. Small Business Administration, Office of Advocacy, based on data provided by the U.S. Census Bureau, Statistic ayroll Small Firm Size Classes, 2007 Revenues per Firm (in $1000s) $ 387,20 $ 1.079,87 $ 1.858,85 $ 2.757,93 $ 3.646,30 $ 4.484,54 $ 5.627,43 $ 6.388,19 $ 7.678,41 $ 8.396,15 $ 11.342,06 $ 16.986,85 $ 24.601,82 $ 36.215,78 $ 50.497,68 $ 73.048,61 $ 101.146,75 $ 131.354,76 $ 214.208,49 $ 271.945,71 $ 451.192,83 $ 577.535,89 $ 1.031.080,28 $ 6.703.445,80 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ Revenue per Employee (in dollars) 233.681,81 164.157,33 158.921,74 164.322,02 167.172,60 167.110,57 176.548,10 173.454,28 183.318,25 179.203,76 188.551,64 198.236,83 203.671,10 210.388,65 208.359,00 212.121,72 226.884,40 216.597,62 248.324,04 223.236,45 261.122,64 259.718,11 296.036,40 327.183,56 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ Total Annual Wages 63.401,86 209.780,28 390.131,74 575.192,33 756.622,68 954.825,11 1.138.442,23 1.345.324,62 1.543.493,26 1.754.871,91 2.253.409,15 3.296.523,15 4.691.350,29 6.848.078,25 9.725.303,60 14.091.308,77 18.467.688,65 24.952.251,72 36.980.905,39 52.797.665,29 78.214.293,77 99.789.225,05 167.000.193,23 970.857.263,10 ded by the U.S. Census Bureau, Statistics of U.S. Businesses. See http://www.sba.gov/advocacy/849/12162 for more information. more information.
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Running head: STATISTICS FINAL ASSIGNMENT: FIRM SIZE AND REVENUES

Statistics Final Assignment: Firm Size and Revenues
Name
Course Title
Instructor
Date

STATISTICS FINAL ASSIGNMENT: FIRM SIZE AND REVENUES

1

STATISTICS FINAL ASSIGNMENT
This assignment has provided me with an opportunity to apply the concepts in a real-life
situation and in the process, develop analytic and practical skills.

A. Determine the correlation between each of the pertinent data labels and justify
why this correlation should be calculated and interpret the correlation you found.
In my view, the significant categories of data are; Midpoint of Firm Size Range, Total
Employment in Category, Revenues per Firm (in $1000s) and Total Annual Wages.
Therefore, shown below is the correlation matrix from excel;

Midpoint of Firm
Size Range
Number of Firms in
Category
Total Employment
in Category
Revenues per Firm
(in $1000s)
Total Annual
Wages

Midpoint of
Firm Size
Range
1

Number of
Firms in
Category

Total
Employment
in Category

Revenues per
Firm (in
$1000s)

-0.111014506

1

0.961242037

0.035298397

1

0.998912417

-0.100548065

0.969185949

1

0.999817738

-0.106619187

0.964578501

0.999609919

Total
Annual
Wages

1

The reason why I found it fit to determine the correlation between Midpoint of Firm Size
Range and Number of Firms in Category was to check whether a relationship existed between
the Midpoint of Firm Size Range and the Num...


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