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
- A 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_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 “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_forward
- 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_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_forwardAn 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_forward
- 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_forwardComposites are materials that are made by embedding a fiber, such as glass or carbon, inside a matrix, such as a metal or a ceramic. Composites are used in engineering structures, and their degradation when subjected to whether conditions is an important issue. In an experiment to investigate the effect of the moisture on a certain kind of composite, the weight gains of a collection of n=28 samples of composite subjected to water diffusion were obtained. The sample mean is x=0.42% with a sample std. of S=0.04% Can we 95% confident from the results of this experiment that the average weight gain for composites of this kind is smaller than 0.43%?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
- Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".† x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 y 334 342 355 363 365 372 381 392 400 412 420 Here is regression output from Minitab: Predictor Constant absorb S = 3.60498 Coef 321.878 156.711 SOURCE Regression Residual Error Total SE Coef 2.483 6.464 R-Sq = 98.5% DF 1 9 10 SS 7639.0 117.0 7756.0 T 129.64 24.24 0.000 0.000 R-Sq (adj) = 98.3% MS 7639.0 13.0 F P 587.81 (a) Does the simple linear regression model appear to be…arrow_forwardWrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t 半 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 334 342 355 363 365 372 381 392 400 412 420 Here is regression output from Minitab: Predictor Coef SE Coef P Constant 321.878 2.483 129.64 0.000 absorb 156.711 6.464 24.24 0.000 S = 3.60498 R-Sq = 98.5% R-Są (adj) - 98.3% SOURCE DF MS F P Regression 1 7639.0 7639.0 587.81 0.000 Residual Error 9 117.0 13.0 Total 10 7756.0 (a) Does the simple linear regression model appear to be…arrow_forwardWrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 y 334 342 355 363 365 372 381 400 392 412 420 Here is regression output from Minitab: Predictor Constant absorb S = 3.60498 Coef 321.878 156.711 SOURCE Regression Residual Error Total R-Sq= 98.5% DF SE Coef 2.483 6.464 1 9 10 SS 7639.0 117.0 7756..0 T 129.64 24.24 P 0.000 0.000. R-Sq (adj) 98.3% MS 7639.0 13.0 F 587.81 (a) Does the simple linear regression model appear to be appropriate?…arrow_forward
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