Question

(1 point) Use software to test the null hypothesis of whether there is a relationship between the two classifications, A and B, of the 3×33×3 contingency table shown below. Test using α=0.05α=0.05. NOTE: You may do this by hand, but it will take a bit of time.

B1B1 | B2B2 | B3B3 | Total | |

A1A1 | 5454 | 4343 | 6868 | 165165 |

A2A2 | 5959 | 6565 | 7272 | 196196 |

A3A3 | 7575 | 6969 | 6565 | 209209 |

Total | 188188 | 177177 | 205205 | 570570 |

(a) χ2=χ2=

(b) Find the degrees of freedom.

(c) Find the critical value. χ2=χ2=

(d) The final conclusion is

**A.** We can reject the null hypothesis that A and B
are not related and accept that there seems to be a relationship
between A and B.

**B.** There is not sufficient evidence to reject the
null hypothesis that there is no relationship between A and B.

Answer #1

a)

Applying chi square test of independence: |

Expected |
E_{i}=row total*column
total/grand total |
B1 | B2 | B3 | Total |

A1 | 54.42 | 51.24 | 59.34 | 165 | |

A2 | 64.65 | 60.86 | 70.49 | 196 | |

A3 | 68.93 | 64.90 | 75.17 | 209 | |

total | 188 | 177 | 205 | 570 | |

chi square χ^{2} |
=(O_{i}-E_{i})^{2}/E_{i} |
B1 | B2 | B3 | Total |

A1 | 0.003 | 1.324 | 1.263 | 2.5906 | |

A2 | 0.493 | 0.281 | 0.032 | 0.8065 | |

A3 | 0.534 | 0.259 | 1.375 | 2.1680 | |

total | 1.0302 | 1.8643 | 2.6706 | 5.5651 | |

test statistic X^{2} = |
5.5651 |

b)

degree of freedom(df) =(rows-1)*(columns-1)= | 4 |

c)

for 4 df and 0.05 level , critical value χ2= | 9.4877 |

d)

**B.** There is not sufficient evidence to reject
the null hypothesis that there is no relationship between A and
B.

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