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 11 obituaries from newspapers from rural towns in Idaho give ?¯=79.68 and ?=2.5. 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) ?0 : _______ ?? : ________(b) Find the test statistic, t =

Answer 1

H₀ :
1 = 77
v/s
НА : > 77

The test statistic is given by,

Vn(X-) T S

  

V11(79.68 – 77) 2.5 = 3.56

Where,

n=11

s=2.5

X = 79.68

The critical value of t at level of significance

g= 0,05

( calculated from t distribution table)

ta,n-1 = 70.05, 11-1 = +0.05.10 1.812

Here, since,

T ta,n-1

We reject the null hypothesis at level of significance

g= 0,05

Hence, we can conclude that this sample provides evidence that people living in Rural Idahho community live longer than 77 years.

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