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)

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that people living in rural Idaho communities live longer than 77
years at 10% level of significance.

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