Question

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 14 obituaries from newspapers from rural towns in Idaho give ?¯=79.83 and ?=2.69. 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 μ , 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)
?0 :  
?? :

(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

Given that, sample size (n) = 14

sample mean = 79.83 and

sample standard deviation (s) = 2.69

a) The null and alternative hypotheses are,

H0 : μ = 77

Ha : μ > 77

b) Test statistic is,

=> Test statistic is, t = 3.936

c) critical value at significance level of 0.10 with degrees of freedom = 14 - 1 = 13 is, t_{​​​​​​crit} = 1.350

Since, test statistic = t = 3.936 > 1.350, we should reject H0.

Yes, this sample provide evidence that people living in rural Idaho communities live longer than 77 years.