Question 9.47

9.47 A reduction in force.

In economic downturns or to improve their competitiveness, corporations may undertake a reduction in force (RIF), in which substantial numbers of employees are laid off. Federal and state laws require that employees be treated equally regardless of their age. In particular, employees over the age of 40 years are a “protected class.” Many allegations of discrimination focus on comparing employees over 40 with their younger coworkers. Here are the data for a recent RIF.

rif1

Over 40
Released No Yes
Yes 8 42
No 503 764
  1. Complete this two-way table by adding marginal and table totals. What percent of each employee age group (over 40 or not) were laid off? Does there appear to be a relationship between age and being laid off?
  2. Perform the chi-square test. Give the test statistic, the degrees of freedom, the P-value, and your conclusion.

9.47

(a) 5.21% of those over 40 and 1.57% of those under 40 were laid off. Yes, it looks like a higher percentage of over 40 were laid off than under 40.
(b) . The data provide evidence of an association between age group and being laid off.