Question

A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over the next 12 months. A categorical response variable showed three options: the company plans to hire and add to the number of employees, the company plans no change in the number of employees, or the company plans to lay off and reduce the number of employees. Another categorical variable indicated if the company was private or public. Sample data for 180 companies are summarized as follows.

Employment Plan	Company
	Private	Public
Add Employees	37	32
No Change	19	34
Lay Off Employees	16	42

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

Answer 1

Solution:

Hypothesis are:

H0: Employment Plan and Company are independent

Vs

H1:  Employment Plan and Company are NOT independent

Sample data for 180 companies are summarized as follows.

Employment Plan	Company
	Private	Public
Add Employees	37	32
No Change	19	34
Lay Off Employees	16	42

Part a) Find the value of the test statistic.

Where

O_ij = Observed frequencies for i^th row and j^th column.

E_ij = Expected frequencies for i^th row and j^th column.

Where

Thus we need to make following table:

Observed Frequencies
	Company
Employment Plan	Private	Public	Total
	37	32	69
Business class	19	34	53
Economy Class	16	42	58
Total	72	108	180

Thus

Thus

Oij	Eij	Oij2/Eij
37	27.600	49.601
32	41.400	24.734
19	21.200	17.028
34	31.800	36.352
16	23.200	11.034
42	34.800	50.690
N = 180

Thus

Chi-square test statistic =

Part b) Find the p-value

df = ( R - 1) X (C - 1)

R = Number of Rows = 3

C = Number of Columns = 2.

df = ( R - 1) X (C - 1)

df = ( 3 - 1) X (2 - 1)

df = 2 X 1

df = 2

Use following Excel command:

=CHISQ.DIST.RT( x , df)

=CHISQ.DIST.RT(9.440 , 2 )

=0.0089

Thus p-value = 0.0089