Question

 

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

Statistical Methods of Business I – Case Study

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.

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.

Answer 1

We will use one way ANOVA in excel to solve it.

ANOVA output:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Bachelor's Degree	30	688.79	22.95966667	12.69222402
High School Diploma	30	367.83	12.261	12.61495414
No High School Diploma	30	313.82	10.46066667	5.612247816
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	2739.276696	2	1369.638348	132.8910519	3.56905E-27	3.101296
Within Groups	896.6633533	87	10.30647533
Total	3635.940049	89

Standard deviation is root of variation. Hence:

Groups	Variance	Standard deviation
Bachelor's Degree	12.69222402	3.562614773
High School Diploma	12.61495414	3.551753671
No High School Diploma	5.612247816	2.369018323

Now, finding confidence intervals (error margins) for 95%

Using descriptive statistic:

Output:

Bachelor's Degree		High School Diploma		No High School Diploma
Mean	22.95966667	Mean	12.261	Mean	10.46066667
Standard Deviation	3.562614773	Standard Deviation	3.551753671	Standard Deviation	2.369018323
Sum	688.79	Sum	367.83	Sum	313.82
Confidence Level(95.0%)	1.330302219	Confidence Level(95.0%)	1.326246617	Confidence Level(95.0%)	0.88460598
Lower 95%	21.62936445	Lower 95%	10.93475338	Lower 95%	9.576060687
Upper 95%	24.28996889	Upper 95%	13.58724662	Upper 95%	11.34527265