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( t₁₈ > 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.