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 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,
Employer Firms, Employment, and Annual Payroll Small Firm Size Classes, 2007
Employment Size of Firm Midpoint of Firm Size Range Number of Firms in Category Total Employment in Category Wages per Employee (in dollars) Revenues per Firm (in $1000s) Revenue per Employee (in dollars) Total Annual Wages
0-4 3,705,275 6,139,463 $38,264.15 $387.20 $233,681.81 $63,401.86
5-9 1,060,250 6,974,591 $31,889.98 $1,079.87 $164,157.33 $209,780.28
10-14 425,914 4,981,758 $33,354.20 $1,858.85 $158,921.74 $390,131.74
15-19 218,928 3,674,424 $34,270.87 $2,757.93 $164,322.02 $575,192.33
20-24 134,254 2,928,296 $34,688.99 $3,646.30 $167,172.60 $756,622.68
25-29 89,643 2,405,637 $35,580.34 $4,484.54 $167,110.57 $954,825.11
30-34 64,753 2,063,987 $35,716.09 $5,627.43 $176,548.10 $1,138,442.23
35-39 47,641 1,754,582 $36,528.71 $6,388.19 $173,454.28 $1,345,324.62
40-44 38,221 1,600,913 $36,850.13 $7,678.41 $183,318.25 $1,543,493.26
45-49 29,705 1,391,754 $37,455.23 $8,396.15 $179,203.76 $1,754,871.91
50-74 86,364 5,195,105 $37,460.92 $11,342.06 $188,551.64 $2,253,409.15
75-99 41,810 3,582,686 $38,470.48 $16,986.85 $198,236.83 $3,296,523.15
100-149 39,316 4,749,055 $38,838.28 $24,601.82 $203,671.10 $4,691,350.29
150-199 18,620 3,205,201 $39,782.60 $36,215.78 $210,388.65 $6,848,078.25
200-299 17,780 4,309,143 $40,127.68 $50,497.68 $208,359.00 $9,725,303.60
300-399 8,155 2,808,347 $40,918.95 $73,048.61 $212,121.72 $14,091,308.77
400-499 4,715 2,101,982 $41,425.26 $101,146.75 $226,884.40 $18,467,688.65
500-749 6,094 3,695,682 $41,145.05 $131,354.76 $216,597.62 $24,952,251.72
750-999 2,970 2,561,972 $42,870.60 $214,208.49 $248,324.04 $36,980,905.39
1,000-1,499 2,916 3,552,259 $43,340.87 $271,945.71 $223,236.45 $52,797,665.29
1,500-1,999 1,542 2,664,416 $45,265.62 $451,192.83 $261,122.64 $78,214,293.77
2,000-2,499 942 2,094,728 $44,875.25 $577,535.89 $259,718.11 $99,789,225.05
2,500-4,999 1,920 6,687,266 $47,947.90 $1,031,080.28 $296,036.40 $167,000,193.23
5,000+ 1,927 39,481,018 $47,385.86 $6,703,445.80 $327,183.56 $970,857,263.10