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A Deloitte employment survey asked a sample of human resourceexecutives how their company planned to change its workforce overthe next 12 months. A categorical response variable showed threeoptions: the company plans to hire and add to the number ofemployees, 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 privateor public. Sample data for 180 companies are summarized asfollows.
| 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 employmentplan for the next 12 months is independent of the type ofcompany.
State the null and alternative hypotheses.
H0: Employment plan is mutually exclusivefrom the type of company.
Ha: Employment plan is not mutually exclusivefrom the type of company.H0: Employment plan isnot independent of the type of company.
Ha: Employment plan is independent of the typeof company.     H0:Employment plan is not mutually exclusive from the type ofcompany.
Ha: Employment plan is mutually exclusive fromthe type of company.H0: Employment plan isindependent of the type of company.
Ha: Employment plan is not independent of thetype of company.
Find the value of the test statistic. (Round your answer tothree decimal places.)
Find the p-value. (Round your answer to four decimalplaces.)
p-value =
At a 0.05 level of significance, what is your conclusion?
Do not reject H0. We cannot conclude thatthe employment plan and the type of company are notindependent.Reject H0. We conclude that theemployment plan is not independent of the type ofcompany.     RejectH0. We conclude that the employment plan isindependent of the type of company.Do not rejectH0. We cannot conclude that the employment planand the type of company are independent.
(b)
Discuss any differences in the employment plans for private andpublic companies over the next 12 months. (Round your numericanswers to two decimal places.)
Employment opportunities look to be much better for publiccompanies, while private companies have the greater proportions of\"no change\" and \"lay off employees\" planned.Employmentopportunities look to be much better for private companies, whilepublic companies have the greater proportions of \"no change\" and\"lay off employees\"planned.     Employment opportunities lookto be about the same for both public and private companies, withhigh proportions of \"no change\" and \"lay off employees\" planned forboth.Employment opportunities look to be about the same for bothpublic and private companies, with high proportions of \"addemployees\" planned for both.
