17.31 Analysis of a reduction in force.
To meet competition or cope with economic slowdowns, corporations sometimes undertake a “reduction in force” (RIF), in which substantial numbers of employees are terminated. Federal and various state laws require that employees be treated equally regardless of their age. In particular, employees over the age of 40 years are in a “protected” class, and many allegations of discrimination focus on comparing employees over 40 with their younger coworkers. Here are the data for a recent RIF:
Over 40 | ||
Terminated | No | Yes |
Yes | 17 | 71 |
No | 564 | 835 |
17.31
(a) . (b) The binomial distribution assumes that each employee's termination is independent from one another's and the probability of being terminated is the same for each employee. Certainly the latter is not true because an individual's performance is likely different and largely determines whether or not they are terminated. (c) , with 95% the confidence interval is (1.644, 4.840). Because the interval does not contain 1, the results are significant at the 5% level. Employees over 40 are 2.82 times more likely to be terminated than those under 40. (d) We could use the additional variables in the logistic regression model to account for their effects before assessing if age has an effect.