Math 207, First Day Activity (Sampling Distributions)—Age Discrimination Case

(This case study is from Watkins, Scheaffer, and Cobb, Statistics in Action: Understanding a World of Data, Key Curriculum Press)

In the spring of 1991, the engineering department (in the envelope division) of Westvaco Corporation had five rounds of layoffs. At the time of the second round of layoffs, there were 10 hourly-wage employees who worked in the engineering department. The ages (in years) of these employees are listed below.

25 33 35 38 48 55 55 55 56 64

During the second round of layoffs, three of the hourly-wage workers were laid off. The ages of these three employees were 55,55, and 64.

Robert Martin, one of the laid-off employees, filed a lawsuit against Westvaco claiming the company practiced age discrimination in deciding who would be laid off during the second round. How can we decide, statistically, whether or not there is strong evidence of age discrimination?

1. Discuss how age discrimination could be shown (or not shown) based on these data. Are there other issues that should be considered besides these ages?

2. What is the average age of the three employees who were laid off? Does this seem high? What are you comparing it to?

3. If there was no age discrimination, then we could possibly assume the ages of the three laid-off employees are simply a random sample from the population of ages (since age has nothing to do with the layoff process). Note: A random sample of size 3 is one where each group of size 3 has the same chance of being the selected sample. As a class, we can simulate this random sampling process, and generate many samples of size 3.

4. Create the population of 10 ages by writing each age on a small piece of paper (simply tear up a piece of notebook or scratch paper). Then mix up the pieces of paper (ages face down)—this process is important to ensure the randomness. Now draw three cards, record the ages as your first sample, and calculate the average age for your sample. (You can do this in the table below.) Repeat this process five times.

Sample	Age 1	Age 2	Age 2	Average Age
1
2
3
4
5

5. Now go to the board and add the sample averages for your 5 random samples to the dot plot.

6. How can we use the distribution of sample averages (on the board) and the group of three employee ages (who were laid off) to decide whether or not there is strong evidence of age discrimination?

This activity illustrates the use of a sampling distribution to make inference. The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population. Sampling distributions are an integral part of this course and an integral part of many statistical analyses.