(2 points) Ann thinks that there is a difference in quality of life between rura
ID: 3067026 • Letter: #
Question
(2 points) Ann thinks that there is a difference in quality of life between rural and urban living. She 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 14 people from rural towns give a life expectancy of 74.5 years with a standard deviation of s,-7.59 years. A sample of 9 people from larger towns give xt = 70.6 years and Su-816 years. Does this provide evidence that people living in rural Idaho communities have different life expectancy than those in more urban communities? Use a 5% level of significance. Assume the populations are normal. mu_u (a) State the null and alternative hypotheses: (Type "mu_r" for the symbol u, , e.g. mu_r not = 0 for the means are not equal, mau-r-mu-u > 0 for the rural mean is larger, mu_r-mu uExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: ?1 = ?2
Alternative hypothesis: ?1 ? ?2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.10. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 3.393
DF = 21
t = [ (x1 - x2) - d ] / SE
t = 1.15
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 21 degrees of freedom is more extreme than -1.15; that is, less than -1.15 or greater than 1.15.
Thus, the P-value = 0.2631
Interpret results. Since the P-value (0.2631) is greater than the significance level (0.05), we cannot accept the null hypothesis.
d) B) The results are significant. The data seems to indicate that people living rural communities have a different life expectancy than those in urban communities.
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