Question

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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

(a)

Conduct a test of independence to determine if the employment plan for the next 12 months is independent of the type of company.

State the null and alternative hypotheses.

H₀: Employment plan is mutually exclusive from the type of company.
H_a: Employment plan is not mutually exclusive from the type of company.H₀: Employment plan is not independent of the type of company.
H_a: Employment plan is independent of the type of company.     H₀: Employment plan is not mutually exclusive from the type of company.
H_a: Employment plan is mutually exclusive from the type of company.H₀: Employment plan is independent of the type of company.
H_a: Employment plan is not independent of the type of company.

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 =

At a 0.05 level of significance, what is your conclusion?

Do not reject H₀. We cannot conclude that the employment plan and the type of company are not independent.Reject H₀. We conclude that the employment plan is not independent of the type of company.     Reject H₀. We conclude that the employment plan is independent of the type of company.Do not reject H₀. We cannot conclude that the employment plan and the type of company are independent.

(b)

Discuss any differences in the employment plans for private and public companies over the next 12 months. (Round your numeric answers to two decimal places.)

Employment opportunities look to be much better for public companies, while private companies have the greater proportions of "no change" and "lay off employees" planned.Employment opportunities look to be much better for private companies, while public companies have the greater proportions of "no change" and "lay off employees" planned.     Employment opportunities look to be about the same for both public and private companies, with high proportions of "no change" and "lay off employees" planned for both.Employment opportunities look to be about the same for both public and private companies, with high proportions of "add employees" planned for both.

Answer 1

.H₀: Employment plan is independent of the type of company.
H_a: Employment plan is not independent of the type of company.

Applying chi square test:

Expected	Ei=row total*column total/grand total	private	Public	Total
	add employee	27.60	41.40	69
	no change	21.20	31.80	53
	lay off	23.20	34.80	58
	total	72	108	180
chi square    χ2	=(Oi-Ei)2/Ei	private	Public	Total
	add employee	3.2014	2.1343	5.336
	no change	0.2283	0.1522	0.381
	lay off	2.2345	1.4897	3.724
	total	5.664	3.776	9.440

value of the test statistic =9.440

p value =0.0089

Reject H₀. We conclude that the employment plan is not independent of the type of company.    

b)

Employment opportunities look to be much better for private companies, while public companies have the greater proportions of "no change" and "lay off employees" planned.