An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
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The authors of a paper randomly selected two samples of patients admitted to the hospital after suffering a stroke. One sample was selected from patients who received biofeedback weight training for 8 weeks, and the other sample was selected from patients who did not receive this training. At the end of 8 weeks, the time it took (in seconds) to stand from a sitting position and then to sit down again (called sit-stand-sit time) was measured for the people in each sample. Data consistent with summary quantities given in the paper are given below. For purposes of this exercise, you can assume that the samples are representative of the population of stroke patients who receive the biofeedback training and the population of stroke patients who do not receive this training.
Biofeedback Group
2.1
2.8
4.5
2.3
2.9
4.3
3.4
4.2
3.4
3.7
3.0
3.7
3.7
2.5
3.3
No Biofeedback Group
5.2
4.8
4.0
4.3
4.8
4.4
4.3
5.2
3.5
4.3
5.2
4.5
4.1
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4.0
Conduct a test of hypothesis to test whether…
Chapter 6 Solutions
An Introduction to Statistical Methods and Data Analysis
Ch. 6.9 - Refer to the oil-spill case study.
What are the...Ch. 6.9 - For each of the situations, set up the rejection...Ch. 6.9 - Conduct a test of H0 : μ1 μ2 – 2.3 versus Ha : μ1...Ch. 6.9 - In an effort to link cold environments with...Ch. 6.9 - The Department of Natural Resources (DNR) received...Ch. 6.9 - An industrial engineer conjectures that a major...Ch. 6.9 - The number of households currently receiving a...Ch. 6.9 - Prob. 9ECh. 6.9 - Refer to Exercise 6.11. There appears to be a...Ch. 6.9 - A firm has a generous but rather complicated...
Ch. 6.9 - Prob. 14ECh. 6.9 - Random samples of size n1 = 8 and n2 = 8 were...Ch. 6.9 - Prob. 16ECh. 6.9 - Prob. 17ECh. 6.9 - The paper Serum Beta-2-Microglobulin (SB2M) in...Ch. 6.9 - Prob. 19ECh. 6.9 - Prob. 20ECh. 6.9 - Prob. 21ECh. 6.9 - Prob. 22ECh. 6.9 - A random sample of eight pairs of twins was...Ch. 6.9 - Refer to the data of Exercise 6.11. A potential...Ch. 6.9 - Researchers are studying two existing coatings...Ch. 6.9 - Prob. 27ECh. 6.9 - The paper “Effect of Long-Term Blood Pressure...Ch. 6.9 - A study was designed to measure the effect of home...Ch. 6.9 - Prob. 30ECh. 6.9 - A random sample of eight pairs of twins were...Ch. 6.9 - Refer to Exercise 6.31. a. What is the level of...Ch. 6.9 - Use the level and power values for the paired t...Ch. 6.9 - Use the level and power values for the paired t...Ch. 6.9 - A study was conducted to determine whether...Ch. 6.9 - The effect of Benzedrine on the heart rate of dogs...Ch. 6.9 - Prob. 37E
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- The authors of a paper randomly selected two samples of patients admitted to the hospital after suffering a stroke. One sample was selected from patients who received biofeedback weight training for 8 weeks, and the other sample was selected from patients who did not receive this training. At the end of 8 weeks, the time it took (in seconds) to stand from a sitting position and then to sit down again (called sit-stand-sit time) was measured for the people in each sample. Data consistent with summary quantities given in the paper are given below. For purposes of this exercise, you can assume that the samples are representative of the population of stroke patients who receive the biofeedback training and the population of stroke patients who do not receive this training. Biofeedback Group 2.2 2.9 4.6 2.4 3.0 4.4 3.5 4.3 3.5 3.8 3.1 3.8 3.8 2.6 3.4 No Biofeedback Group 5.2 4.8 4.0 4.3 4.8 4.4 4.3 5.2 3.5 4.3 5.2 4.5 4.1 3.5 4.0 Conduct a test of hypothesis to test whether…arrow_forwardA 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_forwardIn a clinical trial of 2134 subjects treated with a certain drug, 27 reported headaches. In a control group of 1666 subjects given a placebo, 26 reported headaches. Denoting the proportion of headaches in the treatment group by p, and denoting the proportion of headaches in the control (placebo) group by pe, the relative risk is p,/p.. The relative risk is a measure of the strength of the effect of the drug treatment. Another such measure is the odds ratio, which is the ratio of the odds in favor of a headache for the Pi/ (1-Pt) Po! (1-Pc) treatment group to the odds in favor of a headache for the control (placebo) group, found by evaluating The relative risk and odds ratios are commonly used in medicine and epidemiological studies. Find the relative risk and odds ratio for the headache data. What do the results suggest about the risk of a headache from the drug treatment? Find the relative risk for the headache data. The relative risk = (Round to three decimal places as needed.) Find…arrow_forward
- Researchers wanted to know the effectiveness of a new anti-venom shot. A study was conducted on 245 children who had nonlethal scorpion stings. The ages of the children ranged from 6 months to 18 years old. Each child was randomly assigned to receive a shot of the anti-venom or a placebo shot. Researchers recorded whether or not their condition improved over the next four hours. They found that about 73% of the children who were given anti-venom saw an improvement in their condition whereas only about 23% of the children who were given the placebo saw an improvement in their condition. Identify the population.The population is all children 6 months to 18 years old with nonlethal scorpion stings. Identify the sample.The sample is 245 children 6 months to 18 years old with nonlethal scorpion stings. What is the treatment variable? The treatment variable is the anti-venom shot. What is the response (or outcome) variable?The outcome variable is improvements in their condition.…arrow_forwardA dermatologist compared a new treatment for athlete’s foot (the experimental condition) to the standard treatment (the control condition). He tracked down 30 people with athlete’s foot on both feet and, for each participant, randomly assigned one foot to receive the new treatment and the other foot to receive the standard treatment. After three weeks of treatment, he measured the percent- age of reduction in symptoms (the larger the number, the better the outcome). He found ME = 88, MC = 72, and sD = 8.65.arrow_forwardIn a clinical trial of 2198 subjects treated with a certain drug, 26 reported headaches. In a control group of 1661 subjects given a placebo, 22 reported headaches. Denoting the proportion of headaches in the treatment group by p, and denoting the proportion of headaches in the control (placebo) group by Pc the relative risk is p/pc. The relative risk is a measure of the strength of the effect of the drug treatment. Another such measure is the odds ratio, which is the ratio of the odds in favor of a headache for the treatment group to the odds in favor of a headache for the control (placebo) group, found by evaluating . The relative risk and odds ratios are commonly used in medicine and epidemiological studies. Find the relative risk and odds ratio for the headache data. What do the results suggest about the risk of a headache from the drug treatment? Pt/(1-Pt) Pc/(1-Pc)arrow_forward
- Brink studied the effect of postural change on cardiovascular reactivity for a sample of healthy white and African American men and women. Change in systolic blood pressure (SBP) from supine to standing position was used as the measure of cardiac reactivity in a sample of 842 adults. Supine measurement of blood pressure was taken after participants had lain on an examination table for 15 minutes. Blood pressure was measured five times every 2 minutes using a preset automated blood pressure monitor, and the five measurements were averaged. Participants then stood up, and an additional five measurements were made over another 10-minute period and then averaged. Below is a table describing the characteristics of Brink’s sample. Characteristics of the Study Sample (N = 842) Sample Characteristic Frequency (N) Percentage or Mean (SD) Range Gender Female Male 408 434 48.5% 51.5% Age (years) 842 55.1 (5.3) 44–67 Race/ethnicity White, not Hispanic…arrow_forwardDr. Guidry conducts a study examining the relationship between the number of friends one has and the experience of daily stress and life satisfaction. She randomly samples 1,500 elderly men and women in Nashville, Tennessee (the state capital), located in the southern United States. Below are her findings.• Life satisfaction and experience of daily stress: r = .57 (p = .01)• Number of friends one has and experience of daily stress: r = .09, not sig.• Number of friends one has and life satisfaction: r = .36 (p = .04) Which of the following conclusions can Dr. Guidry draw about the number of friends one has and life satisfaction based on her statistical analyses? a. The probability of her sample coming from a zero association population is about 4%. (correct answer) b. The probability of her sample coming from a zero association population is about 96%. c. The relationship is not statistically significant. d. The strong correlation means that the number of friends one has causes an…arrow_forwardDr. Guidry conducts a study examining the relationship between the number of friends one has and the experience of daily stress and life satisfaction. She randomly samples 1,500 elderly men and women in Nashville, Tennessee (the state capital), located in the southern United States. Below are her findings.• Life satisfaction and experience of daily stress: r = .57 (p = .01)• Number of friends one has and experience of daily stress: r = .09, not sig.• Number of friends one has and life satisfaction: r = .36 (p = .04) In determining whether the relationship between two of Dr. Guidry’s variables was statistically significant, which of the following must be considered? a. Sample size and number of variables analyzed b. Direction of the association and strength of the association c. Sample size and effect size d. The number of outliers and the direction of the association Answer is C. But why? Why,b,c,d are wrong?arrow_forward
- A dietician has developed a new diet which is claimed to reduce LDL cholesterol levels for those who use the diet. The dietician wants to test the diet by sampling a random group of 25 people. The dietician will measure the LDL cholesterol levels of each of the 25 people and then measure their cholesterol levels after people in the sample have used the diet for eight weeks. Which of the following tests would be most appropriate for this study? O a. t-test of one sample O b. t-test of two independent samples O c. z-test of two independent samples O d. t-test of paired samples e. Chi-square test of independencearrow_forwardTo illustrate the effects of driving under the influence of alcohol, a police officer brought a DUI simulator to a high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing special goggles to simulate the effect of alcohol on vision with the following results: Normal: 4.47, 4.24, 4.58, 4.65, 4.31, 4.8, 4.55, 5, 4.79 Impaired: 5.77, 5.67, 5.51, 5.32, 5.83, 5.49, 5.23, 5.61, 5.63 Is there evidence to suggest that there is a difference at alpha = 0.05level of significance.arrow_forwardIn a clinical trial of 2029 subjects treated with a certain drug, 22 reported headaches. In a control group of 1572 subjects given a placebo, 26 reported headaches. Denoting the proportion of headaches in the treatment group by pt and denoting the proportion of headaches in the control (placebo) group by pc, the relative risk is pt/pc. The relative risk is a measure of the strength of the effect of the drug treatment. Another such measure is the odds ratio, which is the ratio of the odds in favor of a headache for the treatment group to the odds in favor of a headache for the control (placebo) group, found by evaluating StartFraction p Subscript t Baseline divided by left parenthesis 1 minus p Subscript t Baseline right parenthesis Over p Subscript c Baseline divided by left parenthesis 1 minus p Subscript c Baseline right parenthesis EndFractionpt/1−ptpc/1−pc. The relative risk and odds ratios are commonly used in medicine and epidemiological studies. Find the relative risk and…arrow_forward
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