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Chapter 10: Q. 10.108 (page 440)
What constitutes each pair in a paired sample?
Each pair constitute the difference between the values of the variable under consideration on the members of the pair.
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Political Prisoners. According to the American Psychiatric Association, posttraumatic stress disorder (PTSD) is a common psychological consequence of traumatic events that involve a threat to life or physical integrity. During the Cold War, some 200,000 people in East Germany were imprisoned for political reasons. Many were subjected to physical and psychological torture during their imprisonment, resulting in PTSD. A. Ehlers et al. studied various characteristics of political prisoners from the former East Germany and presented their findings in the paper "Posttraumatic Stress Dis-order (PTSD) Following Political Imprisonment: The Role of Mental Defeat, Alienation, and Perceived Permanent Change" (Journal of Abnormal Psychology, Vol. 109, pp. 45-55). The researchers randomly and independently selected 32 former prisoners diagnosed with chronic PTSD and 20 former prisoners that were diagnosed with PTSD after release from prison but had since recovered (remitted). The ages, in years, at arrest yielded the following summary statistics.
At the significance level, is there sufficient evidence to conclude that a difference exists in the mean age at arrest of East German prisoners with chronic PTSD and remitted PTSD?
Suppose that you want to perform a hypothesis test to compare the means of two populations, using a paired sample. For each part, decide whether you would use the paired -test, the paired Wilcoxon signed-rank test, or neither of these tests if preliminary data analyses of the sample of paired differences suggest that the distribution of the paired-difference variable is
a. approximately normal.
b. highly skewed; the sample size is .
c. symmetric bimodal.
State the two conditions required for performing a paired r-procedure. How important are those conditions?
Faculty Salaries. Suppose, for example, you want to decide whether the mean salary of faculty in private institutions is greater than the mean salary of faculty in public institutions. State the null and alternative hypotheses for that hypothesis test.
Why do you need to know the sampling distribution of the difference between two sample means in order to perform a hypothesis test to compare two population means?
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