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: 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 yearsWe need to check whether the people living in rural communities live longer than 77 years.So, Hypothesis would be [tex]H_0:\mu=77\\\\H_a:\mu>77[/tex]Since n = 12[tex]\bar{x}=81.03\\\\s=1.53[/tex]since n <30 so, we will use t test.So, the test statistic value is given by[tex]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[/tex]degrees of freedom = df = n-1 = 12-1 =11At 95% significance level , t = 1.796Since, 1.796< 9.125So, we will reject the null hypothesis.Hence, Yes, this sample provide evidence that people living in rural communities live longer than 77 years.