Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 1, Problem 30SE
Compared to their stay-at-home peers, women employed outside the home have higher levels of high-density lipoproteins (HDL), the “good” cholesterol associated with lower risk for heart attacks. A study of cholesterol levels in 2000 women, aged 25–64, living in Augsburg, Germany, was conducted by Ursula Haertel, Ulrigh Keil, and colleagues2 at the GSF-Medis Institut in Munich. Of these 2000 women, the 48% who worked outside the home had HDL levels that were between 2.5 and 3.6 milligrams per deciliter (mg/dL) higher than the HDL levels of their stay-at-home counterparts. Suppose that the difference in HDL levels is
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Chapter 1 Solutions
Mathematical Statistics with Applications
Ch. 1.1 - For each of the following situations, identify the...Ch. 1.2 - Are some cities more windy than others? Does...Ch. 1.2 - Of great importance to residents of central...Ch. 1.2 - The top 40 stocks on the over-the-counter (OTC)...Ch. 1.2 - Given here is the relative frequency histogram...Ch. 1.2 - The relative frequency histogram given next was...Ch. 1.2 - The self-reported heights of 105 students in a...Ch. 1.2 - An article in Archaeometry presented an analysis...Ch. 1.3 - Resting breathing rates for college-age students...Ch. 1.3 - It has been projected that the average and...
Ch. 1.3 - The following results on summations will help us...Ch. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Refer to Exercise 1.3 and repeat parts (a) and (b)...Ch. 1.3 - Refer to Exercise 1.4 and repeat parts (a) and (b)...Ch. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - The manufacturer of a new food additive for beef...Ch. 1 - Prove that the sum of the deviations of a set of...Ch. 1 - The mean duration of television commercials is 75...Ch. 1 - Aqua running has been suggested as a method of...Ch. 1 - The following data give the lengths of time to...Ch. 1 - Prob. 26SECh. 1 - Prob. 27SECh. 1 - The discharge of suspended solids from a phosphate...Ch. 1 - Prob. 29SECh. 1 - Compared to their stay-at-home peers, women...Ch. 1 - Prob. 31SECh. 1 - Prob. 32SECh. 1 - Prob. 33SECh. 1 - Prob. 34SECh. 1 - Prob. 35SECh. 1 - Prob. 36SECh. 1 - Prob. 37SECh. 1 - Prob. 38SE
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- People often wait till middle age to worry about having a healthy heart. However, recent studies have shown that earlier monitoring of risk factors such as blood pressure can be very beneficial (The Wall Street Journal, January 10, 2012). Having higher than normal blood pressure, a condition known as hypertension, is a major risk factor for heart disease. Suppose a large sample of individuals of various ages and gender was selected and that each individual’s blood pressure was measured to determine if they have hypertension. For the sample data, the following table shows the percentage of individuals with hypertension. Develop a side-by-side bar chart with age on the horizontal axis, the percentage of individuals with hypertension on the vertical axis, and side-by-side bars based on gender. What does the display you developed in part (a), indicate about hypertension and age? Comment on differences in gender. Age Male Female 20 - 34 11.0% 9.0% 35 – 44…arrow_forwardThe death rate per 100,000 for lung cancer is 7 among non-smokers and 71 among smokers. The death rate per 100,000 for coronary thrombosis is 422 among non-smokers and 599 among smokers. The prevalence of smoking in the population is 55%. The relative risk of dying for a smoker compared to a non-smoker is: [Refer to the chapter titled “Study Designs: Cohort Studies”] A. 9.1 for lung cancer and 0.30 for coronary thrombosis. B. 10.1 for lung cancer and 1.4 for coronary thrombosis. C. 10.1 for lung cancer and 8.4 for coronary thrombosis. D. 9.1 for lung cancer and 1.4 for coronary thrombosis. E. 12.4 for lung cancer and 1.7 for coronary thrombosis.arrow_forwardA researcher hypothesizes that the lowering in cholesterol associated with weight loss is really due to exercise. To test this, the researcher carefully controls for exercise while comparing the cholesterol levels of a group of subjects who lose weight by dieting with a control group that does not diet. The difference between groups in cholesterol is not significant. Can the researcher claim that weight loss has no effect?arrow_forward
- A medical student at a community college in city Q wants to study the factors affecting the systolic blood pressure of a person (Y). Generally, the systolic blood pressure depends on the BMI of a person (B) and the age of the person A. She wants to test whether or not the BMI has a significant effect on the systolic blood pressure, keeping the age of the person constant. For her study, she collects a random sample of 150 patients from the city and estimates the following regression function: Y= 15.50 +0.90B + 1.10A. (0.48) (0.35) The test statistic of the study the student wants to conduct (Ho: B, =0 vs. H4: B, #0), keeping other variables constant is. (Round your answer to two decimal places.) At the 5% significance level, the student will v the null hypothesis. Keeping BMI constant, she now wants test whether the age of a person (A) has no significant effect or a positive effect on the person's systolic blood pressure. So, the test statistic associated with the one-sided test the…arrow_forwardA case-control study of patients on antihypertensive drugs related an increased risk of myocardial infarction (MI) for patients using calcium channel blockers. In this study, cases were antihypertensive drug patients who had suffered a first fatal or nonfatal Ml through 1993, and controls were antihypertensive drug patients, matched by demographic factors, who had not suffered a MI. Among the comparisons reported were patients receiving calcium channel (CC) blockers (with and without diuretics) and patients receiving B-blockers (with and without diuretics). Results of numbers of patient by drug/MI status combination are given in the following table. Antihypertensive O HO: p1=p2 vs. Ha: p1 p2 vs. Ha: p1=p2 ⒸHO: p1=p2 vs. Ha: p1 = p2 CC blocker B-blocker O HO: p1=p2 vs. Ha: p1 > p2 Occurrence of Yes (cases) 80 85 Drug Does it appear that an increased risk of myocardial infarction (MI) is related to using calcium channel (CC) blockers? The case-control nature of this study requires we…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 (< 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_forwardFor the next items, identity the appropriate statistical test that will be utilized in hypothesis testing. SE T- test T- test (one factor/sample) (Dependent) (Independent) T-test F- Test (Standard Error)arrow_forward
- An important issue is whether there are racial differences in hypertension among children. We define hypertension as being above the 95th percentile for either systolic blood pressure (SBP) or diastolic blood pressure (DBP) among children of the same age, height, and sex. Since some of the children were observed at multiple visits, a GEE model was run of hypertension on ethnic group. There were three ethnic groups considered: Caucasian, African American, and Hispanic. One issue is that BMI, which may vary among ethnic groups, is positively related to hypertension. Hence, a logistic regression model was run, as shown in Table 13.55. 13.89 What is the estimated OR for hypertension comparing Hispanic boys vs. Caucasian boys based on the results in Table 13.55? (Call this OR2 .) Provide a 95% CI for this estimate. 13.90 Suppose the average BMI of Hispanic boys is higher than that for Caucasian boys. Is BMI a confounder of the association between ethnic group and hypertension? If so, is it…arrow_forwardAn important issue is whether there are racial differences in hypertension among children. We define hypertension as being above the 95th percentile for either systolic blood pressure (SBP) or diastolic blood pressure (DBP) among children of the same age, height, and sex. Since some of the children were observed at multiple visits, a GEE model was run of hypertension on ethnic group. There were three ethnic groups considered: Caucasian, African American, and Hispanic. The results among boys are given in Table 13.54. TABLE 13.54 Relationship between hypertension and ethnic group among 27,009 boys in the Pediatric Task Force Data Variable Regression Coefficient SE Intercept -2.07 0.026 African American 0.049 0.041 Hispanic 0.328 0.059 What is the estimated OR for hypertension comparing Hispanic boys vs. Caucasian boys? (Call this OR1.) What is a 95% CI for this estimate?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_forward
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