Mitch thinks that there is a difference in quality of life between rural and urban living. He 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¯=79.1 years with a standard deviation of sr=5.25 years. A sample of 10 people from larger towns give xu¯=75.3 years and su=8.5 years. Does this provide evidence that people living in rural Idaho communities have different life expectancy than those in more urban communities? Use a 1% level of significance.
(a) State the null and alternative hypotheses:
H0 =
Ha =
(b) The degree of freedom is ___.
(c) The test statistic is ___.
(d) Based on this data, Mike concludes:
- There is not sufficient evidence to show that life expectancies are different for rural and urban communities.
- 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.