Question

In this problem, assume that the distribution of differences is
approximately normal. *Note*: For degrees of freedom
*d*.*f*. not in the Student's *t* table, use
the closest *d*.*f*. that is *smaller*. In
some situations, this choice of *d*.*f*. may increase
the *P*-value by a small amount and therefore produce a
slightly more "conservative" answer.

In the following data pairs, *A* represents birth rate and
*B* represents death rate per 1000 resident population. The
data are paired by counties in the Midwest. A random sample of 16
counties gave the following information.

A: |
12.7 | 13.2 | 12.6 | 12.3 | 11.6 | 11.1 | 14.2 | 15.1 |

B: |
9.8 | 14.3 | 10.5 | 14.2 | 13.2 | 12.9 | 10.9 | 10.0 |

A: |
12.5 | 12.3 | 13.1 | 15.8 | 10.3 | 12.7 | 11.1 | 15.7 |

B: |
14.1 | 13.6 | 9.1 | 10.2 | 17.9 | 11.8 | 7.0 | 9.2 |

Do the data indicate a difference (either way) between
population average birth rate and death rate in this region? Use
*α* = 0.01. (Let *d* = *A* − *B*.)

(a) What is the level of significance?

(b) What is the value of the sample test statistic? (Round your answer to three decimal places.)

Answer #1

Solution :

A | B | d = A - B |

12.7 | 9.8 | 2.9 |

13.2 | 14.3 | -1.1 |

12.6 | 10.5 | 2.1 |

12.3 | 14.2 | -1.9 |

11.6 | 13.2 | -1.6 |

11.1 | 12.9 | -1.8 |

14.2 | 10.9 | 3.3 |

15.1 | 10 | 5.1 |

12.5 | 14.1 | -1.6 |

12.3 | 13.6 | -1.3 |

13.1 | 9.1 | 4 |

15.8 | 10.2 | 5.6 |

10.3 | 17.9 | -7.6 |

12.7 | 11.8 | 0.9 |

11.1 | 7 | 4.1 |

15.7 | 9.2 | 6.5 |

a)

Level of Significance *α* = 0.01

b)

**Test Statistic :**

**t = 1.175**

**P-value = 0.25831**

P-value > 0.01

Fail to reject H0 (Null hypothesis)

In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom
d.f. not in the Student's t table, use
the closest d.f. that is smaller. In
some situations, this choice of d.f. may increase
the P-value by a small amount and therefore produce a
slightly more "conservative" answer.
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approximately normal. Note: For degrees of freedom
d.f. not in the Student's t table, use
the closest d.f. that is smaller. In
some situations, this choice of d.f. may increase
the P-value by a small amount and therefore produce a
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