Mike thinks that there is a difference in quality of life between rural and urba
ID: 3218457 • Letter: M
Question
Mike thinks that there is a difference in quality of life between rural and urban living. He collects information from obituaries in newspapers from urban and rural towns in Idaho to see if there is a difference in life expectancy. A sample of 16 people from rural towns give a life expectancy of x_r = 69.9 years with a standard deviation of s_r = 9.37 years. A sample of 5 people from larger towns give x_u = 78.8 years and s_u = 9.26 years. Does this provide evidence that people living in rural Idaho communities have different life expectancy than those in more urban communities? Use a 2% level of significance. Assume the populations are normal. State the null and alternative hypotheses: (Type "mu_r"for the symbol mu_r, e.g. mu_r - mu_u not = 0 for the means are not equal, mu_r - mu_u > 0 for the rural mean is larger, mu_r - mu_uExplanation / Answer
The statistical software output for this problem is:
Two sample T hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0
(with pooled variances)
Hypothesis test results:
Hence,
a) Ho = mu_r - mu_u = 0
H1: mu_r - mu_u not= 0
b) Degrees of freedom = 19
c) Test statistic = -1.8585
d) Since p - value i.e. 0.0787 is greater than 0.02, do not reject the null hypothesis.
Option A is correct.
Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 -8.9 4.7888867 19 -1.8584695 0.0787