Question

(1 point) Sue 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 19 people from rural towns give a life expectancy of xr¯=77.1 years with a standard deviation of sr=5.61 years. A sample of 11 people from larger towns give xu¯=72.8 years and su=9.3 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 μr)

H0 =
Ha =

(b) The degree of freedom is __

(c) The test statistic is __

(d) Based on this data, Sue concludes:

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

Answer 1

a)

Ho: mu_r = mu_u

Ha: mu_r != mu_u (ormu_r ≠ mu_u)

b)

sample mean x =	77.100	72.800
std deviation s=	5.610	9.300
sample size n=	19	11
std error se=s/√n=	1.287	2.804
degree freedom=(se12+se22)2/(se12/(n1-1)+se22/(n2-1))=			14

c)

Point estimate =x1-x2=		4.300
standard error of difference Se=√(S21/n1+S22/n2)=			3.0853
test statistic t =(x1-x2-Δo)/Se=		1.3937

d)

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