Question

In: Statistics and Probability

A Deloitte employment survey asked a sample of human resource executives how their company planned to...

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

1) 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.

-Find the value of the test statistic.

-Find the p-value.

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

A)Reject H0. We conclude that the employment plan is independent of the type of company.

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

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

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

3)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.

A)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.

b)Employment opportunities look to be about the same for both public and private companies, with high proportions of "add employees" planned for both.    

c)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.

d)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.

Solutions

Expert Solution

1) null hypothesis: Ho: employment plan for the next 12 months is independent of the type of company

Alternate hypothesis: Ha: employment plan for the next 12 months is dependent of the type of company

Applying chi square test of independence:
Expected Ei=row total*column total/grand total Private Public Total
add 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 3.201 2.134 5.3357
no change 0.228 0.152 0.3805
lay off 2.234 1.490 3.7241
total 5.6642 3.7762 9.4404
test statistic X2 = 9.440
p value = 0.0089 from excel: chidist(9.44,2)

2)

since p value <0.05

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

3)

c)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.


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