12A sample of human resource executives were asked how their

12.A sample of human resource executives were asked how their company planned to change their work force over the next 12 months. a categorical response variable showed 3 options: add employees, no change, lay off employees. another categorical variable indicated if the company was private or public. Sample data for 180 companies are summarized as followed

(private) add employees 37 no change 19 lay off employees 16

(public add employees 32 no change 34 lay off employees 42

a.)conduct a test of independence to determine if the employment plan for the next 12 months is independent on the type of company.at a .05 level significance what is your conclusion?

b.)discuss any differences in the employment plans for private and public companies over the next 12 months?

Solution

Null hypothesis H₀ : Employment plan for the next 12 months is independent on the type of company

Alternative hypothesis: H_A : Employment plan for the next 12 months is not independent on the type of company

Chi-Square Test

Observed Frequencies

Column variable

Calculations

Row variable

C1

C2

C3

Total

fo-fe

private

37

19

16

72

9.4

-2.2

-7.2

public

32

34

42

108

-9.4

2.2

7.2

Total

69

53

58

180

Expected Frequencies

Column variable

Row variable

C1

C2

C3

Total

(fo-fe)^2/fe

private

27.6

21.2

23.2

72

3.2014

0.2283

2.2345

public

41.4

31.8

34.8

108

2.1343

0.1522

1.4897

Total

69

53

58

180

Data

Level of Significance

0.05

Number of Rows

2

Number of Columns

3

Degrees of Freedom

2

Results

Critical Value

5.991

Chi-Square Test Statistic

9.4404

Calculated chi square value > table value.

The null hypothesis is rejected.

We conclude that employment plan for the next 12 months is not independent on the type of company

b.)discuss any differences in the employment plans for private and public companies over the next 12 months?

Since employment plan for the next 12 months is dependent on the type of company, public and private sector companies should take different plans for the next 12 months.

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
Row variable	C1	C2	C3	Total		fo-fe
private	37	19	16	72		9.4	-2.2	-7.2
public	32	34	42	108		-9.4	2.2	7.2
Total	69	53	58	180
Expected Frequencies
	Column variable
Row variable	C1	C2	C3	Total		(fo-fe)^2/fe
private	27.6	21.2	23.2	72		3.2014	0.2283	2.2345
public	41.4	31.8	34.8	108		2.1343	0.1522	1.4897
Total	69	53	58	180
Data
Level of Significance	0.05
Number of Rows	2
Number of Columns	3
Degrees of Freedom	2
Results
Critical Value	5.991
Chi-Square Test Statistic	9.4404