(1 point) Katie thinks that people living in a rural environment have a healthie

Question

(1 point) Katie 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 17 obituaries from newspapers from rural towns in Idaho give x = 80.48 and s = 1.68. 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 , eg. mu > 1 for the mean is greater than 1, mu

Explanation / Answer

(a)
H0 : mu = 77
Ha : mu > 77

(b)
Standard error of mean = s / sqrt(n) = 1.68 / sqrt(17) = 0.4075
t = (80.48 - 77) / 0.4075 = 8.54

(c)
Critical value of t for df = n-1 = 16 and 90% level of significance is 1.75
As, the observed t (8.54) is greater the critical value, we reject the null hypothesis and conclude that people living in rural Idaho communities live longer than 77 years.
So, the answer is Yes.

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