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 18 obituaries from newspapers from rural towns in Idaho give x¯=77.28 and s=2.66. 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 μμ , 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 Idaho communities live longer than 77 years? (Use a 10% level of significance)

Answer 1

Right Tailed t test, Single Mean

Given: = 77 years, = 77.28 years, s = 2.66 years, n = 18, = 0.10

(a) The Hypothesis:

H0: = 77: The average lifespan in USA is equal to 77 years.

Ha: > 77: The average lifespan in USA is greater than 77 years.

This is a 1 tailed test

(b) The Test Statistic: Since the population standard deviation is unknown, we use the students t test.

The test statistic is given by the equation:

t observed = 0.45

The p Value: The p value (1 tailed) for t = 0.46, for degrees of freedom (df) = n-1 = 17, is; p value = 0.3292

The Critical Value: The critical value (1 Tail) at = 0.01, for df = 17, tcritical= 1.333

The Decision Rule:  

The Critical Value Method: If tobserved is > tcritical or if tobserved is < -tcritical, Then reject H0.

The p-value Method: If P value is < , Then Reject H0.

The Decision:

The Critical Value Method: Since tobserved (0.45) is < t critical (1.333), we Fail to Reject H0.

The p-value Method: Since P value (0.3292) is > (0.10) , We fail to Reject H0.

(c) The Conclusion: There is not sufficient evidence at the 90% significance level to conclude that the average lifespan of the people in Rural Idaho is greater than the average lifespan of the people living in the US.