Concept explainers
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. The article “Properties of Waste Silk Short Fiber/Cellulose Green Composite Films” (J. of Composite Materials, 2012: 123–127) reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.3 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value?
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Chapter 8 Solutions
Probability and Statistics for Engineering and the Sciences
- The article “Effect of Granular Subbase Thickness on Airfield Pavement Structural Response” (K. Gopalakrishnan and M. Thompson, Journal of Materials in Civil Engineering, 2008:331–342) presents a study of the effect of the subbase thickness on the amount of surface deflection caused by aircraft landing on an airport runway. In six applications of a 160 kN load on a runway with a subbase thickness of 864 mm, the average surface deflection was 2.03 mm with a standard deviation of 0.090 mm. Find a 90% confidence interval for the mean deflection caused by a 160 kN load.arrow_forwardA state agency requires a minimum of 5 parts per million (ppm) of dissolved oxygen in order for the oxygen content to be sufficient to support aquatic life. Six water specimens taken from a river at a specific location during the low-water season (July) gave readings of 5.0, 5.0, 5.0, 5.1, 4.9, and 4.6 ppm of dissolved oxygen. Do the data provide sufficient evidence to indicate that the dissolved oxygen content is less than 5 ppm? Test using a = 0.05. State the null and alternative hypotheses. Но: и 5 HoiH = 5 versus H:µ < 5 Ho: u + 5 versus H: µ = 5 Ho: H < 5 versus H: µ = 5 a = 5 versus H: µ + 5 State the test statistic. (Round your answer to three decimal places.) t = -.938 State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) State the conclusion. Ho is not rejected. There is insufficient evidence to conclude that the dissolved oxygen content is less than 5 ppm. H, is rejected. There is sufficient…arrow_forwardThe article "Influence of Freezing Temperature on Hydraulic Conductivity of Silty Clay" (J. Konrad and M. Samson, Journal of Geotechnical and Geoenvironmental Engineering, 2000:180–187) describes a study of factors affecting hydraulic conductivity of soils. The measurements of hydraulic conductivity in units of 108 cm/s (y), initial void ratio (x), and thawed void ratio (x2) for 12 specimens of silty clay are presented in the following table. y 1.01 1.12 1.04 1.30 1.01 1.04 0.955 1.15 1.23 1.28 1.23 1.30 0.84 0.88 0.85 0.95 0.88 0.86 0.85 0.89 0.90 0.94 0.88 0.90 X1 0.81 0.85 0.87 0.92 0.84 0.85 0.85 0.86 0.85 0.92 0.88 0.92 X2 Fit the model y = Bo + fix1 + e. For each coefficient, test the null hypothesis that it is equal to 0. Fit the model y = Bo + Bzx2 + e. For each coefficient, test the null hypothesis that it is equal to 0. Fit the model y = Bo + BzX1 + Bzxz + e. For each coefficient, test the null hypothesis that it is equal to 0. d. Which of the models in parts (a) to (c) is…arrow_forward
- The article “Approximate Methods for Estimating Hysteretic Energy Demand on PlanAsymmetric Buildings” (M. Rathhore, A. Chowdhury, and S. Ghosh, Journal of Earthquake Engineering, 2011: 99–123) presents a method, based on a modal pushover analysis, of estimating the hysteretic energy demand placed on a structure by an earthquake. A sample of 18 measurements had a mean error of 457.8 kNm with a standard deviation of 317.7 kNm. An engineer claims that the method is unbiased, in other words, that the mean error is 0. Can you conclude that this claim is false?arrow_forwardA state agency requires a minimum of 5 parts per million (ppm) of dissolved oxygen in order for the oxygen content to be sufficient to support aquatic life. Six water specimens taken from a river at a specific location during the low-water season (July) gave readings of 4.8, 5.2, 4.8, 4.9, 4.9, and 4.6 ppm of dissolved oxygen. Do the data provide sufficient evidence to indicate that the dissolved oxygen content is less than 5 ppm? Test using ? = 0.05. a) state null and alternate hypotheses b) state the test statistic c) state the rejection region d) state the conclusionarrow_forwardThe article “Effect of Varying Solids Concentration and Organic Loading on the Performance of Temperature Phased Anaerobic Digestion Process” (S. Vandenburgh and T. Ellis, Water Environment Research, 2002:142–148) discusses experiments to determine the effect of the solids concentration on the performance of treatment methods for wastewater sludge. In the first experiment, the concentration of solids (in g/L) was 43.94 ± 1.18. In the second experiment, which was independent of the first, the concentration was 48.66 ± 1.76. Estimate the difference in the concentration between the two experiments, and find the uncertainty in the estimate.arrow_forward
- An article in Environment International ["influence of Water Temperature and Shower Head Office Size on the release Radon During Showering" (1992, Vol. 18(4)] described an experiment in which the amount of radon released in showers was imvestigated. Radon-enriched water was used in the experiment, and six different orifice diameters were tested in shower heads. The data from the experiment are shown in the following table. 5. Orifice Diameter 0.37 0.51 0.71 1.02 Radon Released () 83 75 73 72 83 85 79 79 74 76 77 67 74 74 1.40 62 62 67 69 1.99 60 64 66 (a) Does the size of the orifice affect the mean percentage of radon released? Use a=0.05. (b) Find a 95% confidence interval on the mean percent of radon released when the orifice diameter is 1.40.arrow_forwardThe 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_forward9.48) Acid gases must be removed from other refinery gases in chemical production facilities in order to minimize corrosion of the plants. Two methods for removing acid gases produced the corrosion rates (in mm/yr) are listed below in experimental tests: Method A: 0.3, 0.7, 0.5, 0.8, 0.9, 0.7, 0.8 Method B: 0.7, 0.8, 0.7, 0.6, 2.1, 0.6, 1.4, 2.3 Estimate the difference in mean corrosion rates for the two methods, using a confidence coefficient of 0.90. What assumptions must you make for your answer to be valid?arrow_forward
- Adding glass particles to clay brick may improve the structural properties of the brick. The article "Effects of Waste Glass Additions on the Properties and Durability of Fired Clay Brick" (S. Chidiac and L. Federico, Can J Civ Eng, 2007:1458–1466) describes experiments in which the compressive strength (in MPa) was measured for bricks with varying amounts of glass content and glass particle size. The results in the following table are consistent with means and standard deviations presented in the article. Glass Content (%) Strength (MPa) Size 5 Coarse 78.7 70.8 78.6 81.7 79.2 5 Fine 73.0 90.1 71.4 93.8 82.7 10 Coarse 80.1 76.9 76.5 84.3 77.7 10 Fine 76.2 80.1 121.2 81.4 61.2 15 Coarse 90.3 95.8 103.1 99.5 73.3 15 Fine 141.1 144.1 122.4 134.5 124.9 a. Estimate all main effects and interactions. b. Construct an ANOVA table. You may give ranges for the P-values. Is the additive model plausible? Provide the value of a test statistic and the P-value. Can the effect of glass content on…arrow_forwardLactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk production. The paper “Bone Mass Is Recovered from Lactation to Postweaning in Adolescent Mothers with Low Calcium Intakes” (Amer. J. of Clinical Nutr., 2004:1322-1326) gave the following data on total body bone mineral content (TBBMC) (g) for a sample both during lactation (L) and in postweaning period (P). (Let = true mean difference in TBBMC, postweaning minus lactation.) Subject 1 2 3 4 5 6 7 8 9 10 L 1928 2549 2825 1924 1628 2175 2114 2621 1843 2541 P 2126 2885 2895 1942 1750 2184 2164 2626 2006 2627 Does the data suggest that true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g? State and test the appropriate hypotheses using a significance level of .05. [Note: The appropriate normal probability plot shows some curvature but not enough to…arrow_forwardThe article "Effect of Granular Subbase Thickness on Airfield Pavement Structural Response" (K. Gopalakrishnan and M. Thompson, Journal of Materials in Civil Engineering, 2008:331-342) presents a study of the amount of surface deflection caused by aircraft landing on an airport runway. A load of 160 kN was applied to a runway surface, and the amount of deflection in mm (y) was measured at various distances in m (x) from the point of application. The results are presented in the following table. y 0.000 3.24 0.305 2.36 0.610 1.42 0.914 0.87 1.219 0.54 1.524 0.34 1.830 0.24 a. Fit the linear model y = Bo + B1x + ɛ. For each coefficient, test the hypothesis that the coefficient is equal to 0. b. Fit the quadratic model y = Bo + Bịx + B2x² + ɛ. For each coefficient, test the hypothesis that the coefficient is equal to 0. %3D Fit the cubic model y = Bo + B1x + B2x? + B3x + E. For each coefficient, test the C. hypothesis that the coefficient is equal to 0. d. Which of the models in parts (a)…arrow_forward
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