Question

In economic downturns or to improve their competitiveness, corporations may undertake a "reduction in force" (RIF), where substantial numbers of employees are released. 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 Over 40 No Yes Released Yes No 7 44 504 762 (a) Complete this two-way table by adding marginal and table totals. Over 40 Released Yes No Totals No Yes Totals 6 40 505 766 What percent of each employee age group (over 40 or not) were released? Under 40 Over 40 Does there appear to be a relationship between age and being released? yes no (b) Perform the chi-square test. Give the test statistic, the degrees of freedom, the P-value, and your conclusion x2 P-value Conclusion Reject Ho. There is evidence that there is a relationship between employee's age and being released O Do not reject Ho. There is evidence that there is a relationship between employee's age and being released O Reject Ho. There is no evidence that there is a relationship between employee's age and being released. Do not reject Ho. There is no evidence that there is a relationship between employee's age and being released

Answer 1

a) From the given data

Observed Frequencies
	Over 40
Released	No	Yes	Total
Yes	6	40	46
No	505	766	1271
Total	511	806	1317

The percentage of each employee age group were released is, uder 40, 511/1317 = 0.388 = 38.8%
The percentage of each employee age group were released is, Over 40, 806/1317 = 0.612 = 61.2%

The relation between age and being released is Yes
Answer: Yes

b)

The expected frequencies are
	Over 40
Released	No	Yes	Total
Yes	17.848	28.152	46
No	493.152	777.848	1271
Total	511	806	1317

The Chi-Square contribution values are

Oi	Ei	(Oi-Ei)^2 /Ei
6	17.848	7.865
40	28.152	4.9863
505	493.152	0.2846
766	777.848	0.1805
	Total:	13.3164

Test Statistic, X^2: 13.3168

Degrees of freedom: 1

P-Value: 0.0003

Here P-value < alpha 0.05 so we reject H0

Correct Answer: Option (A) There is evidence that there is a relationship between employee's age and being released