Question

Ben 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 9 obituaries from newspapers from rural towns in Idaho give x¯=77.98 and s=1.27. 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 μμ , e.g. mu >1 for the mean is greater than 1, mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1)
H0 :
Ha :

(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)

Answer 1

Part a)

H0 :- µ = 77
H1 :- µ > 77

Part b)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 77.98 - 77 ) / ( 1.27 / √(9) )
t = 2.315

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.1 , 9-1) = 1.397
t > t(α, n-1) = 2.315 > 1.397
Result :- Reject null hypothesis

Part c)

Yes, sample provide enough evidence to prove that people living in rural Idaho communities live longer than 77 years at 10% level of significance.