Question

Ann 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 9 people from rural towns give a life expectancy of xr¯=81.7 years with a standard deviation of sr=5.88 years. A sample of 7 people from larger towns give xu¯=74.1 years and su=9.07 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: (Type ‘‘mu_r′′ for the symbol μr , e.g. mu_rnot=mu_u for the means are not equal, mu_r>mu_u for the rural mean is larger, mu_r

H0H0 =
HaHa =

(b) The degree of freedom is

(c) The test statistic is

(d) Based on this data, Ann 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.

Answer 1

given,

$\mu_r = 81.7$

0r = 5.88

ny 7

$\mu_u = 74.1$

$\sigma_u = 9.07$
Hypothesis,

$H_0 : \mu_r = \mu_u$

$H_1 : \mu_r \neq \mu_u$

also,

level of significance,

degree of freedom,

The test statistic is given by,

$t = \frac{\mu_r-\mu_u}{\sqrt{\frac{\sigma_r^{2}}{n_r} + \frac{\sigma_u^{2}}{n_u}}}$

t = 1.9246

t critical at 0.01 level of significance is,

tcrit = 3.7070

therefore,

since, t < | tcrit |, we fail to reject H0

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