13.9 Custom Woodworking, Inc., has been in business for 40 years. The company produces high-quality custommade wooden furniture and very high quality interior cabinet and interior woodwork for expensive homes and offices. It has been very successful in large part because of the highly skilled craftworkers, who design and produce its products in consultation with customers.

Many of the company’s products have won national awards for quality design and artisanship. Each custom-made product is produced by a team of two or more craftworkers who first meet with the customer, prepare an initial design, review the design with the customer, and then build the product. Customers may also meet with the craftworkers at various times during the production.

The craftworkers are well educated and have developed excellent woodworking skills. Most have liberal arts degrees and have trained with skilled craftworkers.

Employees are classified at three levels: 1, apprentice;

2, professional; and 3, master. Levels 2 and 3 pay higher wages, and workers typically move through the levels as they gain experience and skill. The company now has a diverse workforce, which includes white, black, and Latino workers and both men and women.

When the business started 40 years ago, all workers were white males. About 20 years ago the company began to hire black and Latino craftworkers, and about 10 years ago they hired women craftworkers. The white male workers tend to be overrepresented in the higher job classifications because, in part, they have the most experience. At present, the workforce contains 40% white males, 30% black and Latino males, 15%
white females, and 15% black and Latino females.
Recently, serious concerns have been expressed concerning wage discrimination. Specifically, it is alleged that women and nonwhite workers are not receiving fair compensation based on their experience.
The company management claims that every person is paid fairly based on years of experience, job classification level, and individual ability. It claims that there are no differences in wages based on either race or gender in terms of either base wage or increment for each year of experience.
Explain how you would carry out an analysis to determine if management’s claim is true. Show the details of your analysis and provide a clear rationale.
Indicate the data that should be collected and the names and descriptions of the variables you will use in the analysis. Clearly indicate the statistical tests that would be used to determine the true situation and indicate the decision rules based on the hypothesis tests and results from the data.