Question

Academic staff members at a college were cross-classified
according to gender and political affiliation. The two-way table
below shows the results.

Democrat | Republican | R total | |

Male | 39 | 19 | |

Female | 85 | 26 | |

C total | 169 |

Calculate the marginal counts (row and column totals) in the table.
Then, conduct a test to determine whether gender and political
affiliation are independent at the significance level of 0.1.

(a) State the null and alternative hypotheses.

H0:H0: Gender and political affiliation select are are
not independent.

Ha:Ha: Gender and political affiliation select are are
not independent.

(b) Calculate the expected counts. (Round to 3 decimal
places.)

Democrat | Republican | |

Male | ||

Female |

(c) Calculate the test statistic.

(Round to 3 decimal places.)

(d) Approximate the p-value.

select p-value < 0.01 0.01 < p-value < 0.05 0.05 <
p-value < 0.10 p-value > 0.10

(e) State the decision.

select Reject Fail to reject the null hypothesis.

Answer #1

a)

H0: Gender and political affiliation are independent.

Ha: Gender and political affiliation are not independent.

b)

Observed | |||

Democrat | Republican | total | |

Male | 39 | 19 | 58 |

Female | 85 | 26 | 111 |

Total | 124 | 45 | 169 |

Expected count = sum(rowi)*sum(coli)/total

for example, expected count for democrat and male = 124*58/169 = 42.56

Expected | ||

Democrat | Republican | |

Male | 42.56 | 15.44 |

Female | 81.44 | 29.56 |

c)

Test statistic, chi-square = sum((Oi - Ei)^2/Ei) = 1.699

d)

p-value > 0.10

e)

Fail to reject H0

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