Question

# Ann thinks that there is a difference in quality of life between rural and urban living....

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 12 people from rural towns give a life expectancy of xr¯=74.4years with a standard deviation of sr=7.54years. A sample of 17 people from larger towns give xu¯=74.6x years and su=5.04years. Does this provide evidence that people living in rural Idaho communities have different life expectancy than those in more urban communities? Use a 5% level of significance.

(a) State the null and alternative hypotheses: (Type ‘‘mu_r′′‘‘mu_r″ for the symbol μrμr , e.g. mu_rnot=mu_umu_rnot=mu_u for the means are not equal, mu_r>mu_umu_r>mu_u for the rural mean is larger, mu_r<mu_umu_r<mu_u , for the rural mean is smaller. )

H0H0 =
HaHa =

(b) The degree of freedom is

(c) The test statistic is

Given data,

nr = 12

nu = 17

sr = 7.54

su = 5.04

xr¯=74.4

xu¯=74.6

level of significance α = 5%

(a)

null and alternative hypotheses:

H0: mu_r = mu_u

Ha: mu_r not = mu_u

(b)

Degrees of freedom:

= 17.8145

~ 18

(c)

test statistic:

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