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 12 obituaries from newspapers from rural towns in Idaho give x¯=81.03 and s=1.53. 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) H0 : Ha:

(b) Find the test statistic, t =

Answer 1

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

Step-by-step explanation:

Since we have given that

Average lifespan in the USA = 77 years

We need to check whether the people living in rural communities live longer than 77 years.

So, Hypothesis would be

$H_0:\mu=77\\\\H_a:\mu>77$

Since n = 12

$\bar{x}=81.03\\\\s=1.53$

since n <30 so, we will use t test.

So, the test statistic value is given by

$t=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\\\t=\dfrac{81.03-77}{\dfrac{1.53}{\sqrt{12}}}\\\\\\t=\dfrac{4.03}{0.4416}\\\\t=9.125$

degrees of freedom = df = n-1 = 12-1 =11

At 95% significance level , t = 1.796

Since, 1.796< 9.125

So, we will reject the null hypothesis.

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