Concept explainers
Nondestructive evaluation. Nondestructive evaluation (NDE) describes methods that quantitatively characterize materials, tissues, and structures by noninvasive means, such as X-ray computed tomography, ultrasonics, and acoustic emission. Recently, NDE was used to detect defects in steel castings (JOM, May 2005). Assume that the probability that NDE detects a “hit” (i.e., predicts a defect in a steel casting) when, in fact, a defect exists is .97. (This is often called the probability of detection.) Also assume that the probability that NDE detects a hit when, in fact, no defect exists is .005. (This is called the probability of a false call.) Past experience has shown a defect occurs once in every 100 steel castings. If NDE detects a hit for a particular steel casting, what is the probability that an actual defect exists?
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Statistics for Business and Economics (13th Edition)
- Patients with rheumatoid arthritis are at a greater risk of developing osteoporosis. The reasons are not well understood due to the difficulty in qualitatively assessing bone metabolism and mineral content. A researcher measures human calcitonin (HCT) levels in men with rheumatoidarthritis. The researcher randomly selects 43 men with rheumatoid arthritis and measured the mean HCT level of 33.8 pg/mL. Assume that HCT for individuals with rheumatoid arthritis follows a normal distribution with standard deviation σ = 23.6 pg/mL.1. For a 95% level of confidence what is the appropriate critical value Z*that needs to beused to calculate the margin of error? Determine the value of the critical value using a table or preferred technological tool.arrow_forwardDefine and explain Type I and Type II errors and relate each to the selection of an alpha level.arrow_forwardPatients with rheumatoid arthritis are at a greater risk of developing osteoporosis. The reasons are not well understood due to the difficulty in qualitatively assessing bone metabolism and mineral content. A researcher measures human calcitonin (HCT) levels in men with rheumatoidarthritis. The researcher randomly selects 43 men with rheumatoid arthritis and measured the mean HCT level of 33.8 pg/mL. Assume that HCT for individuals with rheumatoid arthritis follows a normal distribution with standard deviation σ = 23.6 pg/mL. 7. Describe a situation where a researcher would want to use a larger confidence level than 95% and a situation where a smaller confidence level would be preferred.arrow_forward
- Left ventricular mass (LVM) is an important risk factor for subsequentcardiovascular disease. A study is conducted to assess the relationship between the size of LVM in children (as determined from an echocardiogram) and the size of LVM four years later in the same individuals. Does LVM change over time in children? Completely conduct the appropriate hypothesis and list any additional necessary assumptions (you can assume that additional assumptions are met by the data) test with alpha =0.01. i Baseline LVM LVM 4 years later 1 134 126 2 86 142 3 78 111 4 73 82arrow_forwardAs the alpha level gets lower, which error rate also gets lower? Type I Type IIarrow_forwardMinimization of false trends in measurement caused by extraneous variables can be minimized by: A. Randomizing the order of application of the independent variable. B. Repeated measurement of the dependent variables. C. Signal conditioning and recalibration of the test instrument. D. Neglecting controlled parametrization of fundamental features of the test instrument. E. Getting a new replacement of the test instrument.arrow_forward
- Heat flow is the passage of thermal energy from a hot to a cold body. This phenomenon is of particular interest to engineers, who attempt to understand and control the flow of heat through the use of thermal insulation and other devices. The data below were taken from heat flow gauge readings for an industrial process over 10 equally spaced time intervals. A concern is that the process may be cooling down as time progresses. One way to check this statistically is to compare the measurements for the first 5 time periods to the measurements for the last 5 time periods. You may assume that heat flow is approximately normal for each group. Time period 1 (Group 1): 9.273, 9.262, 9.243, 9.283, 9.270Time period 2 (Group 2): 9.240, 9.292, 9.284, 9.279, 9.258 Unless otherwise stated, give your answers to three decimal places. Construct a 95% confidence interval for the difference in mean heat flow. Give your answers to three decimal places. Use t∗=2.352t∗=2.352.( , ) Conduct a hypothesis…arrow_forwardContaminated water: Polychlorinated biphenyls (PCBS) are a group of synthetic oil-like chemicals that were at one time widely used as insulation in electrical equipment and were discharged into rivers. They were discovered to be a health hazard and were banned in the 1970s. Assume that water samples are being drawn from a river in order to estimate the PCB concentration. Suppose that a random sample of size 65 has a sample mean of 1.95 parts per billion (ppb). Assume the population standard deviation is o=0.41 ppb. Part: 0 / 3 Part 1 of 3 (a) Construct a 98% confidence interval for the PCB concentration. Use tables or technology. Round your answers to at least two decimal places. OD- The confidence interval isarrow_forwardContaminated water: Polychlorinated biphenyls (PCBS) are a group of synthetic oil-like chemicals that were at one time widely used as insulation in electrical equipment and were discharged into rivers. They were discovered to be a health hazard and were banned in the 1970s. Assume that water samples are being drawn from a river in order to estimate the PCB concentration. Suppose that a random sample of size 89 has a sample mean of 1.81 parts per billion (ppb). Assume the population standard deviation is o=0.44 ppb. Part: 0 / 3 Part 1 of 3 (a) Construct a 98% confidence interval for the PCB concentration. Use tables or technology. Round your answers to at least two decimal places. CD: The confidence interval is NOV 1 W MacBook Air 80 888 DII DD F2 F3 F4 F5 F6 F7 F8 F9 F10 $ &arrow_forward
- Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items produced. If they find a significant increase in the proportion of items that must be rejected, they will halt the assembly process until the problem can be identified and repaired. State the hypotheses: In this context, what is a type I error? What is a consequence of this error? In this context, what is a type II error? What is a consequence of this error? Which type of error would the factory owner consider more serious? Which type of error might customers consider more serious?arrow_forwardMultiple myeloma, or blood plasma cancer, is characterized by increased blood vessel formulation (angiogenesis) in the bone marrow that is a predictive factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient's own stem cells. The data show below represents the bone marrow microvessel density for patients who has a complete response to the stem cell transplant (as measured by blood and urine tests). The measurements were taken immediately prior to the stem cell transplant and at the time the complete response was determined. Patient Before After 1 158 284 2 186 214 3 202 101 4 353 227 5 416 290 6 426 176 7 441…arrow_forwardContaminated water: Polychlorinated biphenyls (PCBS) are a group of synthetic oil-like chemicals that were at one time widely used as insulation in electrical equipment and were discharged into rivers. They were discovered to be a health hazard and were banned in the 1970s. Assume that water samples are being drawn from a river in order to estimate the PCB concentration. Suppose that a random sample of size 80 has a sample mean of 1.90 parts per billion (ppb). Assume the population standard deviation is o = 0.26 ppb. Part 1 of 3 ▬▬ esc (a) Construct a 98% confidence interval for the PCB concentration. Use tables or technology. Round your answers to at least two decimal places. The confidence interval is 1.83 1.97 Part 2 of 3 Skip Part Check Type here to search 12 2 # * 3 14 $ 4 D Et % 5 6 & 7 4+ Save For Later © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center 55°F 8 9 ho Submit. ► 11 d 1 3/arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman