Question

(1 point) Sue thinks that there is a difference in quality of life between rural and urban living. She collects information from obituaries in newspapers from urban and rural towns in Idaho to see if there is a difference in life expectancy. A sample of 19 people from rural towns give a life expectancy of xr¯=77.1 years with a standard deviation of sr=5.61 years. A sample of 11 people from larger towns give xu¯=72.8 years and su=9.3 years. Does this provide evidence that people living in rural Idaho communities have different life expectancy than those in more urban communities? Use a 2% level of significance.

(a) State the null and alternative hypotheses: (Type ‘‘mu_r″ for the symbol μr)

H0 =

Ha =

(b) The degree of freedom is __

(c) The test statistic is __

(d) Based on this data, Sue concludes:

**A.** There is not sufficient evidence to show that
life expectancies are different for rural and urban
communities.

**B.** The results are significant. The data seems to
indicate that people living in rural communities have a different
life expectancy than those in urban communities.

Answer #1

a)

Ho: mu_r = mu_u

Ha: mu_r != mu_u (ormu_r ≠ mu_u)

b)

sample mean x = | 77.100 | 72.800 | |

std deviation s= | 5.610 | 9.300 | |

sample size n= | 19 | 11 | |

std error se=s/√n= | 1.287 | 2.804 | |

degree
freedom=(se_{1}^{2}+se_{2}^{2})^{2}/(se_{1}^{2}/(n_{1}-1)+se_{2}^{2}/(n_{2}-1))= |
14 |

c)

Point estimate =x1-x2= | 4.300 | ||

standard
error of difference
Se=√(S^{2}_{1}/n_{1}+S^{2}_{2}/n_{2})= |
3.0853 | ||

test statistic t
=(x_{1}-x_{2}-Δ_{o})/Se= |
1.3937 |

d)

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