Andrew thinks that people living in a rural environment have a healthier lifestyle than other people. He believes the average lifespan in the USA is 77 years. A random sample of 18 obituaries from newspapers from rural towns in Idaho give \(\bar{x} = 78.92\) and \(s = 2\text{.}\) Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years?

(a) State the null and alternative hypotheses: (Type "mu" for the symbol \(\mu\) , e.g. mu \(>\)1 for the mean is greater than 1, mu \(\lt \) 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1)

\(H_0\) :

\(H_a\) :

(b) Find the test statistic, t =

(c) Answer the question: Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years? (Use a 10% level of significance)

(Type: Yes or No)