In: Statistics and Probability

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 *H*_{0}. We conclude that the employment
plan is independent of the type of company.

b)Do not reject *H*_{0}. We cannot conclude that
the employment plan and the type of company are not
independent.

c) Reject *H*_{0}. We conclude that the
employment plan is not independent of the type of company.

d)Do not reject *H*_{0}. 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.

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 |
E_{i}=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 χ^{2} |
=(O_{i}-E_{i})^{2}/E_{i} |
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 X^{2} = |
9.440 |
|||

p value = |
0.0089 |
from excel: chidist(9.44,2) |

2)

since p value <0.05

c) Reject *H*_{0}. 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.

A Deloitte employment survey asked a sample of human resource
executives how their company planned to change its workforce over
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or the company plans to lay off and reduce the number of employees.
Another categorical variable indicated if the company was private
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