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Wire electrical-discharge machining (WEDM) is a process used to manufacture conductive hard metal components. It uses a continuously moving wire that serves as an electrode. Coating on the wire electrode allows for cooling of the wire electrode core and provides an improved cutting performance. The article “High-Performance Wire Electrodes for Wire Electrical-Discharge Machining—A Review” (J. of Engr. Manuf., 2012: 1757–1773) gave the following sample observations on total coating layer thickness (in μm) of eight wire electrodes used for WEDM:
Calculate a 99% CI for the standard deviation of the coating layer thickness distribution. Is (his interval valid whatever the nature of the distribution? Explain.
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Chapter 7 Solutions
Probability and Statistics for Engineering and the Sciences
- Stressed-Out Bus Drivers. Previous studies have shown that urban bus drivers have an extremely stressful job, and a large proportion of drivers retire prematurely with disabilities due to occupational stress. In the paper, “Hassles on the Job: A Study of a Job Intervention With Urban Bus Drivers” (Journal of Organizational Behavior, Vol. 20, pp. 199–208), G. Evans et al. examined the effects of an intervention program to improve the conditions of urban bus drivers.Amongother variables, the researchers monitored diastolic blood pressure of bus drivers in downtown Stockholm, Sweden. The data, in millimeters of mercury (mm Hg), on the WeissStats site are based on the blood pressures obtained prior to intervention for the 41 bus drivers in the study. Use the technology of your choice to do the following. a. Obtain a normal probability plot, boxplot, histogram, and stemand-leaf diagram of the data. b. Based on your results from part (a), can you reasonably apply the one-mean t-test to the…arrow_forwardclassify as either observational or experimental design Heart Failure. In the paper “Cardiac-Resynchronization Therapy with or without an Implantable Defibrillator in Advanced Chronic Heart Failure” (New England Journal of Medicine, Vol. 350, pp. 2140–2150), M. Bristow et al. reported the results of a study of methods for treating patients who had advanced heart failure due to ischemic or nonischemic cardiomyopathies. A total of 1520 patientswere randomly assigned in a 1:2:2 ratio to receive optimal pharmacologic therapy alone or in combination with either a pacemaker or a pacemaker–defibrillator combination. The patients were thenobserved until they died or were hospitalized for any cause.arrow_forwardAn experiment to determine the effect of four different types of engine oil (A, B, C, and D) on the rolling friction coefficient of a car speed has been conducted. Three brands of car (Honda, Toyota, and Mazda) were chosen, and each engine oil was tested twice on each car, producing the following ANOVA output in Figure 2. i) How many treatments involved? Write down all the treatments ii) Identify the number of replication for each treatment. iii) Based on the ANOVA table above, find the values of W, X, Y and Z. iv) Test the interaction effect on rolling friction coefficient of car speed between the four different types of engine oil and the three different brands of car. v) Do we need to test for marginal effect? Give a reason.arrow_forward
- A new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set up and interpret the results of a Mann-Whitney U test with an alpha of .05. Pain Rating as Reported by Patients Old Drug 1 2 2 4 6 New Drug 1 2 2 3 7 Old Drug New Drug Total Sample (Ordered Smallest to Largest) Ranks Old Drug New Drug Old Drug New Drug 1 1 1 1 1.5 1.5 2 2 2 2 4.5 4.5 2 2 2 2 4.5 4.5 4 3 3 7 6 7 4 8 6…arrow_forwardA new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set up and interpret the results of a Mann-Whitney U test with an alpha of .05. Pain Rating as Reported by PatientsOld Drug 1 2 2 4 6 New Drug 1 2 2 3 7Old Drug New Drug Total Sample(Ordered Smallest to Largest) RanksOld Drug New Drug Old Drug New DrugR1= R2= A) We reject H0 in favor of H1, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 12.5 is greater than the critical U value of 2.B) We reject H0 in favor of H1, which states the two populations are not equal at the alpha equals .05…arrow_forwardA new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set up and interpret the results of a Mann-Whitney U test with an alpha of .05. Pain Rating as Reported by Patients Old Drug 1 2 2 4 6 New Drug 1 2 2 3 7 Old Drug New Drug Total Sample (Ordered Smallest to Largest) Ranks Old Drug New Drug Old Drug New Drug 1 1 1 1 1.5 1.5 2 2 2 2 4.5 4.5 2 2 2 2 4.5 4.5 4 3 3 7 6 7 4 8 6…arrow_forward
- A new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set up and interpret the results of a Mann-Whitney U test with an alpha of .05. Pain Rating as Reported by Patients Old Drug 1 3 3 4 6 New Drug 1 2 3 3 7arrow_forwardA new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set up and interpret the results of a Mann-Whitney U test with an alpha of .05. Pain Rating as Reported by Patients Old Drug 1 3 3 4 6 New Drug 1 2 3 3 7 Old Drug New Drug Total Sample (Ordered Smallest to Largest) Ranks Old Drug New Drug Old Drug New Drug…arrow_forwardA new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set up and interpret the results of a Mann-Whitney U test with an alpha of .05. Pain Rating as Reported by Patients Old Drug 1 3 3 4 6 New Drug 1 2 3 3 7 Old Drug New Drug Total Sample (Ordered Smallest to Largest) Ranks Old Drug New Drug Old Drug New Drug…arrow_forward
- A new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set up and interpret the results of a Mann-Whitney U test with an alpha of .05. Pain Rating as Reported by Patients Old Drug 1 3 3 4 6 New Drug 1 2 3 3 7 A) We fail to reject H0, which states the two populations are equal at the alpha equals .05 level because the calculated Uvalue of 10.5 is greater than the critical U value of 2. B) We fail to reject H0, which states the two populations are equal at the alpha equals .05 level…arrow_forwardA study was conducted to examine if children with autism spectrum disorder (ASD) had higher prenatal exposure to air pollution, specifically particulate matter < 2.5 g in diameter (PM2.5). Researchers obtained birth records of all children born in Los Angeles between 2000 and 2008 and linked these to the Department of Developmental Services records to determine if any of those subjects had been diagnosed with ASD or not. They used the birth addresses given in the birth records to determine the average daily PM2.5 for the third trimester for each child. The standard deviation for PM2.5 among ASD subjects was found to be 34.6 and for non-ASD subjects was 16.8. Assume PM2.5 is normally distributed. 4a. What was the study design? * Randomized Clinical Trial (RCT) * Case Report * Nested Case-Control Study * Case-Control Study * cross-sectional study Cohort Study 4B. What are the null and alternative hypotheses? 4c. What type of statistical test would you use to analyze the…arrow_forwardThe article “Differences in Susceptibilities of Different Cell Lines to Bilirubin Damage” (K. Ngai, C. Yeung, and C. Leung, Journal of Paediatric Child Health, 2000:36–45) reports an investigation into the toxicity of bilirubin on several cell lines. Ten sets of human liver cells and 10 sets of mouse fibroblast cells were placed into solutions of bilirubin in albumin with a 1.4 bilirubin/albumin molar ratio for 24 hours. In the 10 sets of human liver cells, the average percentage of cells surviving was 53.9 with a standard deviation of 10.7. In the 10 sets of mouse fibroblast cells, the average percentage of cells surviving was 73.1 with a standard deviation of 9.1. Find a 98% confidence interval for the difference in survival percentages between the two cell lines.arrow_forward
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