An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Chapter 12.3, Problem 1Q
To determine
The pairwise comparisons for the heart rate data of Case Study 12.2.1 at the 0.05 level of significance.
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Blood cocaine concentration (mg/L) was determinedboth for a sample of individuals who had died fromcocaine-induced excited delirium (ED) and for a sampleof those who had died from a cocaine overdose withoutexcited delirium; survival time for people in bothgroups was at most 6 hours. The accompanying datawas read from a comparative boxplot in the article“Fatal Excited Delirium Following Cocaine Use” (J.of Forensic Sciences, 1997: 25–31).
ED 0 0 0 0 .1 .1 .1 .1 .2 .2 .3 .3.3 .4 .5 .7 .8 1.0 1.5 2.7 2.83.5 4.0 8.9 9.2 11.7 21.0Non-ED 0 0 0 0 0 .1 .1 .1 .1 .2 .2 .2.3 .3 .3 .4 .5 .5 .6 .8 .9 1.01.2 1.4 1.5 1.7 2.0 3.2 3.5 4.14.3 4.8 5.0 5.6 5.9 6.0 6.4 7.98.3 8.7 9.1 9.6 9.9 11.0 11.512.2 12.7 14.0 16.6 17.8
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Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood-pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 90th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the two groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period.
To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 1 .
Table 1 Pilot data on left ventricular mass (LVM) in children from the Bogalusa Heart Study
ID
Baseline LVM (g)
4- year LVM (g)
Change (g)*
1
139
163
24
2
134
126
-8
3
86
142
56…
Chapter 12 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 12.2 - Prob. 1QCh. 12.2 - Mount Etna erupted in 1669, 1780, and 1865 (recall...Ch. 12.2 - An indicator of the value of a stock relative to...Ch. 12.2 - Each of five varieties of corn are planted in...Ch. 12.2 - Prob. 5QCh. 12.2 - Prob. 6QCh. 12.2 - Prob. 7QCh. 12.2 - Prob. 8QCh. 12.2 - Prob. 9QCh. 12.2 - Verify the conclusion of Example 12.2.2 by doing a...
Ch. 12.2 - Prob. 12QCh. 12.2 - Prob. 13QCh. 12.3 - Prob. 1QCh. 12.3 - Prob. 2QCh. 12.3 - Intravenous infusion fluids produced by three...Ch. 12.3 - Construct 95%Tukey intervals for all ten pairwise...Ch. 12.3 - Prob. 5QCh. 12.3 - Prob. 6QCh. 12.3 - Prob. 7QCh. 12.4 - The cathode warm-up time (in seconds) was...Ch. 12.4 - Test the hypothesis that the average of the true...Ch. 12.4 - In Case Study 12.2.1 test the hypothesis that the...Ch. 12.4 - Prob. 4QCh. 12.4 - Prob. 5QCh. 12.4 - For many years sodium nitrite has been used as a...Ch. 12.5 - Prob. 1QCh. 12.5 - Prob. 2QCh. 12.5 - Three air-to-surface missile launchers are tested...
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- True or False: For both AIC and BIC (two statistics we often use to compare model fit), the model with higher values of AIC or BIC is considered a better fit to the data.arrow_forwardTo examine bivariate data graphically, the best choice is two side by side histograms? Define this statement?arrow_forwardLeft ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood-pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 90th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the two groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 1 . Table 1 Pilot data on left ventricular mass (LVM) in children from the Bogalusa Heart Study ID Baseline LVM (g) 4- year LVM (g) Change (g)* 1 139 163 24 2 134 126 -8 3 86 142 56…arrow_forward
- Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood-pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 90th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the two groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 1 . Table 1 Pilot data on left ventricular mass (LVM) in children from the Bogalusa Heart Study ID Baseline LVM (g) 4- year LVM (g) Change (g)* 1 139 163 24 2 134 126 -8 3 86 142 56…arrow_forwardLeft ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood-pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the two groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 9.18 (Note: These are the same data as in Table 8.27, p. 329). 9.68 What is the critical region at the 5% level? (i.e., for what values of the test statistic will we reject H0 at the 5% level?)…arrow_forwardLeft ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood-pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the two groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 9.18 (Note: These are the same data as in Table 8.27, p. 329). 9.65 Suppose the investigators are reluctant to assume that the change in LVM over four years is normally distributed. What test…arrow_forward
- Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood-pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the two groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 9.18 (Note: These are the same data as in Table 8.27, p. 329). 9.71 Compare your results in Problems 9.69 and 9.70. 9.72 Compare your results to those obtained using t test methods in Problem…arrow_forwardLeft ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood-pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height)and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the two groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after4 years of follow-up. The data are given in images. a) Suppose the investigators are reluctant to assume that the change in LVM over four years is normally distributed. What test can be used to assess if there is a change in mean LVM over four…arrow_forwardLeft ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood-pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height)and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the two groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after4 years of follow-up. The data are given in images. Problem a)What is the two-sided p-value for this test?Problem b)Now perform the test using the exact method andobtain a 2-sided p-value.Problem c) Compare your results in Problems a and b.arrow_forward
- Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood-pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the two groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period.To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 9.18. A)Suppose the investigators are reluctant to assume that the change in LVM over four years is normally distributed. What test can be used to assess if there is a change in mean LVM over…arrow_forwardThe effectiveness of surgery for weight loss reported here found that "The surgery was associated with significantly greater weight loss [than the control group who dieted] through 2 years (61.3 versus 11.2 pounds, P<0.001)." What test could have been used and how would it have been computed?arrow_forward
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