Question

Texas is home to more than one million undocumented immigrants, and most of them are stuck in low-paying jobs. Meanwhile, the state also suffers from a lack of skilled workers. The Texas Workforce Commission estimates that 133,000 jobs are currently unfilled, many because employers cannot find qualified applicants (The Boston Globe, September 29, 2011). Texas was the first state to pass a law that allows children of undocumented immigrants to pay in-state college tuition rates if they have lived in Texas for three years and plan to become permanent residents. The law passed easily back in 2001 because most legislators believed that producing college graduates and keeping them in Texas benefits the business community. In addition, since college graduates earn more money, they also provide the state with more revenue.

Chuck Norris, who sits on the Board of Directors for the Texas Workforce Commission suggests the board should hire your consulting firm, Stat Solutions, to estimate the mean hourly wage of workers with various levels of education. You accept the job and a sample is collected of the hourly wages of 30 Texas workers with a bachelor’s degree or higher, 30 Texas workers with only a high school diploma, and 30 Texas workers who did not finish high school.

Chuck wants you to provide a full report for him to present at the next meeting of the Texas Workforce Commission Board of Directors which occurs in 10 days.

Requirements and associated point values:

Part 1 – Calculate and use descriptive statistics to compare hourly wages for each of the education levels. Be sure to include the mean, standard deviation and margin of error with 95% confidence for each of the 3 levels (9 calculations). These calculations range in value from 3-4 points each for a total of 33 points. Note: See page 293 for the margin of error formula.

Part 2 – Construct and interpret 95% confidence intervals for the mean hourly wage at each education level. There should be an upper and lower number for each of the 3 levels. The end result should be 6 numbers which are valued at 3 points each for a total of 18 points.

Part 3 - Write up your findings in report form. For an example review and refer to other reports throughout your textbook. There is at least one at the end of each chapter. In your report discuss the difference between the means, etc. What do you find? Does education seem to make a difference? Remember these are dollar value wages. Please note: you are expected to use proper statistical terminology when appropriate but remember you are writing for a group who may not be as knowledgeable about statistics as you are. You must be sure they can understand your findings while also writing a professional report. This portion of the case study is valued at 29 points. Of those points, 9 will be allocated to proper grammar and spelling.

Data File and Grading Rubric

The data file for the case study is in an Excel spreadsheet and located in Blackboard, see “Case Study.” The grading rubric is on the second sheet of the Excel workbook. The submission link is located in the same folder. Refer to the course schedule for the case study due date.

Excel

You are expected to use Excel functions for the majority of your calculations. 10 points are allocated to the use of Excel. I will check within the cells to find/confirm your formulas and summation. An additional 10 points are allocated to showing your work (calculations). If you use Excel you receive the combined amount (20 points). If you perform the calculations by hand and show your work on paper you will receive only 10 points. Use Excel! It is a great tool that will serve you well in your future endeavors. The case study is valued at a total of 100 points.

Bachelor's Degree	High School Diploma	No High School Diploma
22.50	12.68	11.21
19.57	11.23	8.54
24.13	19.53	12.52
27.23	9.85	9.06
27.00	15.76	14.21
28.60	12.31	13.40
16.85	12.27	11.46
22.70	8.57	11.22
26.69	11.06	9.56
20.14	11.47	9.43
21.33	13.38	10.98
18.33	9.85	10.41
17.86	12.35	11.73
20.47	10.68	8.28
21.08	10.70	8.59
17.05	11.54	13.30
21.70	13.55	7.91
22.19	17.80	12.28
23.80	15.70	10.72
22.30	17.50	15.97
22.42	6.50	10.58
22.29	8.98	9.59
27.43	12.14	10.92
23.14	8.83	9.70
22.84	13.02	7.64
21.86	8.90	10.39
29.32	13.80	4.62
26.00	21.67	13.04
30.53	8.74	6.29
21.44	7.47	10.27

Case Study Grading Rubric	Possible Points
Correctly calculated 3 means * 3 points each	9
Correctly calculated 3 standard deviations * 4 points each	12
Correctly calculated 3 margin of error * 4 points each	12
Calculate Confidence Interval for education level 1- 3 points each	6
Calculate Confidence Interval for education level 2	6
Calculate Confidence Interval for education level 3	6
Show calculations	10
Use Excel formulas and summation functions	10
Written report/discussion of findings	20
Proper grammar, spelling and terminology in report	9
Total points possible	100

Answer 1

The means of bachelor's degree, high school diploma and no high school diploma are 22.95967,12.261and 10.16067 respectively. The standard deviations of bachelor's degree, high school diploma and no high school diploma are 3.562615,3.551754 and 2.890694 respectively. The margin errors of each type respectively are 0.650441,0.648459,0.527766. The confidence intervals at 0.05 level of significance for each type respectively are (21.68482,24.23451),(10.99004,13.53196) and (9.12664,11.19507).