Mike 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 13 people from rural towns give a life expectancy of $\bar{x_r} = 81.4$ years with a standard deviation of $s_r = 7.67$ years. A sample of 6 people from larger towns give $\bar{x_u} = 84.3$ years and $s_u = 6.09$ 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 $\mu_r$ , e.g. $mu\_r \; not = mu\_u$ for the means are not equal, $mu\_r > mu\_u$ for the rural mean is larger, $mu\_r < mu\_u$ , for the rural mean is smaller. )
$H_0$ =
$H_a$ =

(b) The degree of freedom is

(c) The test statistic is

(d) Based on this data, Mike concludes:

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