Question

Lois thinks that people living in a rural environment have a healthier lifestyle than other people. She believes the average lifespan in the USA is 77 years. A random sample of 19 obituaries from newspapers from rural towns in Idaho give x¯=77.58x¯=77.58 and s=1.69s=1.69. 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 ?? , 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)

H0H0 :

HaHa :

(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

a) As we are trying to test the claim whether the sample provide evidence that people living in rural Idaho communities live longer than 77 years, therefore the null and the alternative hypothesis here are given as:

b) The test statistic here is computed as:

**Therefore 1.4960 is the test statistic value
here.**

c) For n - 1 = 18 degrees of freedom, we get from the t distribution tables that:

p - P( t_{18} > 1.4960) = 0.0760

**Therefore 0.0760 is the p-value here.**

As the p-value is 0.0760 < 0.1 which is the level of
significance, therefore the test is significant and we can reject
the null hypothesis here and conclude that this provides enough
evidence that people living in rural Idaho communities live longer
than 77 years. **Yes is the correct answer here.**

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