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Chapter 10: Q.10.141 (page 444)
Explain exactly how a paired -test can be formulated as a onemean-test. (Hint: Work solely with the paired-difference variable.)
The null hypothesis is rejected since the numbers fall within the critical range, indicating that people prefer Nibbles to Wribbles.
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Two-Tailed Hypothesis Tests and CIs. As we mentioned on page 413, the following relationship holds between hypothesis tests and confidence intervals: For a two-tailed hypothesis test at the significance level , the null hypothesis will be rejected in favor of the alternative hypothesis if and only if the ( )-level confidence interval for does not contain . In each case, illustrate the preceding relationship by comparing the reults of the hypothesis test and confidence interval in the specified xercises.
a. Exercises 10.48 and 10.54.
b. Exercises 10.49 and 10.55.
Fortified Juice and PIH. Refer to Exercise 10.47 and find a 90% confidence interval for the difference between the mean reductions in PTH levels for fortified and unfortified orange juice.
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 the sample sizes, and , are equal for independent simple random samples from two populations.
a. Show that the values of the pooled and nonpooled r-statistics will be identical. (Hint: Refer to Exercise 10.61 on page 417.)
b. Explain why part (a) does not imply that the two t-tests are Equivalent (i.e., will necessarily lead to the same conclusion) when the sample sizes are equal.
Acute Postoperative Days. Refer to Example (page 420). The researchers also obtained the following data on the number of acute postoperative days in the hospital using the dynamic and static systems.
At the significance level, do the data provide sufficient evidence to conclude that the mean number of acute postoperative days in the hospital is smaller with the dynamic system than with the static system? (Note: and )
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