Question

Analysis of the rate of turnover of employees by a personnel manager produced the following table showing the length of stay of 200 people who left the company for other employment. Use a 1% significance level to test whether length of employment is independent of grade.

Length of employment (years)

Grade

0-2

2-5

>5

Managerial

4

11

6

Skilled

32

28

21

Unskilled

25

23

50

Analysis of the rate of turnover of employees by a personnel manager produced the following table showing the length of stay of 200 people who left the company for other employment. Use a 1% significance level to test whether length of employment is independent of grade.

	Length of employment (years)
Grade	0-2	2-5	>5
Managerial	4	11	6
Skilled	32	28	21
Unskilled	25	23	50

Answer 1

Null hypothesis: Ho : length of employment is independent of grade

Alternate hypothesis:Ha: : length of employment is dependent of grade

degree of freedom(df) =(rows-1)*(columns-1)=		4
for 4 df and 0.01 level,critical value χ2=		13.277
Decision rule : reject Ho if value of test statistic X2>13.277

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	0-2	2-5	>5	Total
	Managerial	6.405	6.510	8.085	21
	Skilled	24.705	25.110	31.185	81
	Unskilled	29.890	30.380	37.730	98
	total	61	62	77	200
chi square    χ2	=(Oi-Ei)2/Ei	0-2	2-5	>5	Total
	Managerial	0.903	3.097	0.538	4.5375
	Skilled	2.154	0.333	3.326	5.8131
	Unskilled	0.800	1.793	3.990	6.5830
	total	3.8572	5.2222	7.8544	16.9337
test statistic X2=		16.934
p value =	0.0020	from excel: chidist(16.9337,4)

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that length of employment is dependent of grade