Concept explainers
The vulnerability of inshore environments to contamination due to urban and industrial expansion in Mombasa is discussed in the paper “Metals, Petroleum Hydrocarbons and Organochlorines in Inshore Sediments and Waters on Mombasa, Kenya” [Marine Pollution Bulletin (1997) 34:570–577]. A geochemical and oceanographic survey of the inshore waters of Mombasa, Kenya, was undertaken during the period from September 1995 to January 1996. In the survey, suspended particulate matter and sediment were collected from 48 stations within Mombasa’s estuarine creeks. The concentrations of major oxides and 13 trace elements were determined for a varying number of cores at each of the stations. In particular, the lead concentrations in suspended particulate matter (mg kg−1 dry weight) were determined at 37 stations. The researchers were interested in determining whether the average lead concentration was greater than 30 mg kg−1 dry weight. The data are given in the following table along with summary statistics and a normal probability plot.
Lead concentrations (mg kg−1 dry weight) from 37 stations in Kenya
- a. Is there sufficient evidence (α = .05) in the data that the
mean lead concentration exceeds 30 mg kg−1 dry weight? - b. What is the probability of a Type II error if the actual mean concentration is 50?
- c. Do the data appear to have a
normal distribution ? - d. Based on your answer in (c), is the
sample size large enough for the test procedures to be valid? Explain.
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An Introduction to Statistical Methods and Data Analysis
- The authors of the article “Predictive Model for PittingCorrosion in Buried Oil and Gas Pipelines”(Corrosion, 2009: 332–342) provided the data on whichtheir investigation was based.a. Consider the following sample of 61 observations onmaximum pitting depth (mm) of pipeline specimensburied in clay loam soil. 0.41 0.41 0.41 0.41 0.43 0.43 0.43 0.48 0.480.58 0.79 0.79 0.81 0.81 0.81 0.91 0.94 0.941.02 1.04 1.04 1.17 1.17 1.17 1.17 1.17 1.171.17 1.19 1.19 1.27 1.40 1.40 1.59 1.59 1.601.68 1.91 1.96 1.96 1.96 2.10 2.21 2.31 2.462.49 2.57 2.74 3.10 3.18 3.30 3.58 3.58 4.154.75 5.33 7.65 7.70 8.13 10.41 13.44Construct a stem-and-leaf display in which the twolargest values are shown in a last row labeled HI.b. Refer back to (a), and create a histogram based oneight classes with 0 as the lower limit of the firstclass and class widths of .5, .5, .5, .5, 1, 2, 5, and 5,respectively.c. The accompanying comparative boxplot fromMinitab shows plots of pitting depth for four differenttypes of soils.…arrow_forwardIn a study conducted in the Science Department of Faculty of Science, Technology and Human Development in a University; the researcher examined the influence of the drug succinylcholine on the circulation levels of androgens in the blood. Blood samples from wild, free-ranging deer were obtained via the jugular vein immediately after an intramuscular injection of succinylcholine using darts and a capture gun. Deer were bled again approximately 30 minutes after the injection and then released. The level of androgens at time of capture and 30 minutes later, measured in nanograms per milliliter (ng/ml), for 15 deers as in Table Q1. Assuming that the populations of androgen at time of injection and 30 minutes later are normally distributed:i) Find the average and standard deviation of this studyii)Determine the critical region of this problem.iii) Test at the 0.05 level of significance whether the androgen concentrations are altered after 30 minutes of restraint.arrow_forwardAn article in Knee Surgery, Sports Traumatology, Arthroscopy, "Arthroscopic meniscal repair with an absorbable screw: results and surgical technique," (2005, Vol. 13, pp. 273-279) cites a success rate of 1% for meniscal tears with a rim width of less than 3 mm, and a 1% success rate for tears from 3-6 mm. If you are unlucky enough to suffer a meniscal tear of less than 3 mm on your left knee, and one of width 3-6 mm on your right knee, what is the probability that you have exactly one successful surgery? assume surgieries are independent.arrow_forward
- classify 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_forwardHigh levels of blood sugar are associated with an increased risk of type 2 diabetes. A levelhigher than normal is referred to as “impaired fasting glucose.” The article “Association ofLow-Moderate Arsenic Exposure and Arsenic Metabolism with Incident Diabetes andInsulin Resistance in the Strong Heart Family Study” (M. Grau-Perez, C. Kuo, et al.,Environmental Health Perspectives, 2017, online) reports a study in which 47 of 155 peoplewith impaired fasting glucose had type 2 diabetes. Consider this to be a simple randomsample. a) Find a 95% confidence interval for the proportion of people with impaired fasting glucose who have type 2 diabetes. b) Find a 99% confidence interval for the proportion of people with impaired fasting glucose who have type 2 diabetes. c) A doctor claims that less than 35% of people with impaired fasting glucose have type 2 diabetes. With what level of confidence can this claim be made?arrow_forwardStressed-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_forward
- The paper “Effect of long-term blood pressure control on salt sensitivity” [Journal of Medicine (1997) 28:147–156] describes a study evaluating salt sensitivity (SENS) after a period of antihypertensive treatment. Ten hypertensive patients (diastolic blood pressure between 90 and 115 mmHg) were studied after at least 18 months on antihypertensive treatment. SENS readings, which were obtained before and after the patients were placed on an antihypertensive treatment, are given in the table. 'Before' 'After' 22.86 6.11 7.74 -4.02 15.49 8.04 9.97 3.29 1.44 -0.77 9.39 6.99 11.4 10.19 1.86 2.09 -6.71 11.4 6.42 10.7 a) Write the null and alternate hypotheses What test will be used to test the hypothesis and what assumptions are required? test them. Is there significant evidence that the mean SENS value decreased after the patient received antihypertensive treatment?arrow_forwardThe article “Drift in Posturography Systems Equipped with a Piezoelectric Force Platform: Analysis and Numerical Compensation” (L. Quagliarella, N. Sasanelli, and V. Monaco, IEEE Transactions on Instrumentation and Measurement, 2008: 997–1004) reported the results of an experiment to determine the effect of load on the drift in signals derived from a piezoelectric force plate. The correlation coefficient y between output and time under a load of 588 N was −0.9515. Measurements were taken 100 times per second for 300 seconds, for a total of 30,000 measurements. Find a 95% confidence interval for the population correlation ρ.arrow_forwardFollowing are the protein contents measured in two types of species:Species 1: 0.72 1.12 0.81 0.89 0.72 0.81 1.01 0.75 0.83Species 2: 1.21 0.93 0.80 1.12 1.22 0.94 0.87 i) Assuming normality, test the hypothesis that the two species have the sameaverage protein contents by using 5-step hypothesis testing procedure at 5 %level of significance, and using the critical values approach.ii) Calculate the p-value of this test and make decision.iii) Write down the standard error of this test and calculate its numerical value ?arrow_forward
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