Ben thinks that people living in a rural environment have a healthier lifestyle

Question

Ben thinks that people living in a rural environment have a healthier lifestyle than other people. He believes the average lifespan in Canada is 77 years. A random sample of 8 obituaries from newspapers from rural towns in Canada give x¯=79.49 and s=1.39. Does this sample provide evidence that people living in rural 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 communities live longer than 77 years? (Use a 10% level of significance)
(Type: Yes or No)

Explanation / Answer

1) Ho: =77

Ha: >77

here degree of freedom =n-1=7

for 7df and 0.10 level and right tailed test critical value t =1.4149

Deciison rule: reject Ho: if test stat t>1.4149

here std error =std deviation/(n)1/2 =1.39/(8)1/2 =0.4914

hence test statistic t=(X-mean)/std error =(79.49-77)/0.4914=5.0668~ 5.07

c) as test statistic is in critical region ; therefore this sample provide evidence that people living in rural communities live longer than 77 years

hence Yes,

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