Question 1113100: Sam 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 18 people from rural towns give a life expectancy of xr¯=77.6 years with a standard deviation of sr=8.19 years. A sample of 10 people from larger towns give xu¯=71.7 years and su=9.59 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. Assume the populations are normal.
(a) State the null and alternative hypotheses: (Type ‘‘mu_r′′ for the symbol μr , e.g. mu_r−mu_u not=0 for the means are not equal, mu_r−mu_u>0 for the rural mean is larger, mu_r−mu_u<0 , for the rural mean is smaller. )
H0 = ?
Ha = ?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Ho: mu_r - mu_u = 0
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Ha: mu_r - mu_u > 0
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This is a one-tailed test
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standard error(SE) = square root( ((8.19)^2/18) + ((9.59)^2/10) ) = 3.5949
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Degrees of Freedom is the lesser of (18-1) and (10-1) = 9
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t-statistic is (77.6 - 71.7) / 3.5949 = 1.6412
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Use student's t-table or a t-distribution calculator
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Probability(T< or = 1.6412) = 0.9324
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since 0.9324 is > 0.01, we can not reject Ho
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