Question

Sue thinks that there is a difference in the 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 16 people from rural towns gives a life expectancy of xr¯=82.3 years with a standard deviation of sr=6 years. A sample of 10 people from larger towns gives xu¯=83.4 years and su=6.77 years. Does this provide evidence that people living in rural Idaho communities have different life expectancy than those in more urban communities? Use a 10% level of significance.

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

H0 =

Ha=

(b) The degree of freedom is

(c) The test statistic is

Answer 1

a) H₀:

    H_a:

b) DF = (s_r²/n₁ + s_u²/n₂)²/((s_r²/n₁)²/(n₁ - 1) + (s_u²/n₂)²/(n₂ - 1))

         = ((6)^2/16 + (6.77)^2/10)^2/(((6)^2/16)^2/15 +((6.77)^2/10)^2/9)

         = 17

c) The test statistic t = ()/sqrt(s_r²/n₁ + s_u²/n₂)

                                 = (82.3 - 83.4)/sqrt((6)^2/16 + (6.77)^2/10)

                                = -0.42