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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. Company Employment Plarn Private Public Add Employees No Change Lay Off Employees 37 32 19 34 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. Ho: Employment plan is not independent of the type of company Ha: Employment plan is independent of the type of company HO: Employment plan is independent of the type of company Ha: Employment plan is not independent of the type of company. Ho: Employment plan is mutually exclusive from the type of company Ha: Employment plan is not mutually exclusive from the type of company O HO: Employment plan is not mutually exclusive from the type of company Ha: Employment plan s mutualy xclusive from 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-

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Answer #1

(a)

Second option is correct.

Following table shows the row total and column total:

Total 32 Private Public Add Employees No Change Lay off Employees Total 37 19 16 72 69 53 58 180 42 108

Expected frequencies will be calculated as follows:

ith row total ith row total Eij 20 grand total

Following table shows the expected frequencies:

Private Public Total Add Employees No Change Lay off Employees Total 27.6 21.2 23.2 72 41.4 31.8 34.8 108 69 53 58 180
Following table shows the calculations for chi square test statistics:

37 19 16 32 34 42 (О-Е)^2/Е 27.6 3.201449275 21.2 0.228301887 23.2 2.234482759 41.4 2.134299517 31.8 0.152201258 34.8 1.48965
Following is the test statistics:

9.44

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (3-1)*(2-1)=2

The p-value is : 0.0089

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