State the null and alternate hypotheses and find the degree of freedom.

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 11 people from rural towns give a life expectancy of xr¯=68.4 years with a standard deviation of sr=7.04 years. A sample of 10 people from larger towns give xu¯=74.4 years and su=6.23 years. 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″ 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<mu_u , for the rural mean is smaller. )
H0 = ?

Null hypotheses always contain the equal sign. Therefore the null hypothesis is that the two means are equal and the alternative hypothesis is that the two means are different.

Next, not sure how you calculated the standard deviation for the combined sample. Once again, happy to send you the formula for pooled and un-pooled variance because your answers are incorrect.

Finally, your conclusions are incorrect. We do not have enough evidence to reject the null.

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