Question

A political scientist obtained recordings of election-night acceptance speeches of seven newly elected representatives to the U.S. Congress and counted the number of minutes devoted to urban problems in these speeches. Four of these representatives were from rural districts. They devoted 5, 0, 3, and 4 minutes to urban problems. The other three representatives, who were from urban districts, devoted 11, 11, and 14 minutes to urban problems. Do these results suggest that the amount of time devoted to urban problems in acceptance speeches of newly elected representatives to the U.S. Congress differ according to whether they come from rural or urban districts? (Use the .05 level.)

Use the five steps of hypothesis testing

Answer #1

The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

Rural | Urban | |

3.00 | 12.00 | mean |

2.16 | 1.73 | std. dev. |

4 | 3 | n |

5 | df | |

-9.000 | difference (Rural - Urban) | |

4.000 | pooled variance | |

2.000 | pooled std. dev. | |

1.528 | standard error of difference | |

0 | hypothesized difference | |

-5.892 | t | |

.0020 | p-value (two-tailed) |

The p-value is 0.0020.

Since the p-value (0.0020) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the amount of time devoted to urban problems in acceptance speeches of newly elected representatives to the U.S. Congress differ according to whether they come from rural or urban districts.

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