The article “The Influence of Corrosion Inhibitor and Surface Abrasion on the Failure of Aluminum-Wired Twist-On Connections” (IEEE Trans. on Components, Hybrids, and Manuf. Tech., 1984: 20–25) reported data on potential drop measurements for one sample of connectors wired with alloy aluminum and another sample wired with EC aluminum. Does the accompanying SAS output suggest that the true average potential drop for alloy connections (type 1) is higher than that wfor EC connections (as stated in the article)? Carry out the appropriate test using a significance level of .01. In reaching your conclusion, what type of error might you have committed? [Note: SAS reports the P-value for a two-tailed test.]
Type | N | Mean | Std Dev | Std Error |
1 | 20 17.49900000 | 0.55012821 | 0.12301241 | |
2 | 20 16.90000000 | 0.48998389 | 0.10956373 | |
Variances | T DF | Prob>|T| | ||
Unequal | 3.6362 37.5 | 0.0008 | ||
Equal | 3.6362 38.0 | 0.0008 |
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Chapter 9 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- 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_forwardThe article "Change in Creep Behavior of Plexiform Bone with Phosphate Ion Treatment" (R. Regimbal, C. DePaula, and N. Guzelsu, Bio-Medical Materials and Engineering, 2003:11-25) describes an experiment to study the effects of saline and phosphate ion solutions on mechanical properties of plexiform bone. The following table presents the yield stress measurements for six specimens treated with either saline (NaCI) or phosphate ion (Na,HPO4) solution, at a temperature of either 25°C or 37°C. (The article presents means and standard deviations only; the values in the table are consistent with these.) Solution Temperature NaCl Yield Stress (MPa) 138.40 130.89 94.646 96.653 116.90 88.215 25°C NaCl 37°C 92.312 147.28 116.48 88.802 114.37 90.737 Na,HPO, 25°C 120.18 129.43 139.76 132.75 137.23 121.73 Na,HPO4 37°C 123.50 128.94 102.86 99.941 161.68 136.44 a. Estimate all main effects and interactions. b. Construct an ANOVA table. You may give ranges for the P-values. Is the additive model…arrow_forwardStructural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863-872) desaribes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical modes, the system was underdamped (damping ratio 1)? Explain why or why not f. e. For what damping ratio would you predict a frequency of 2.0?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_forwardCaptopril is a drug designed to lower systolic blood pressure. When subjects were treated with this drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. Results are given in the accompanying table (based on data from “Essential Hypertension: Effect of an Oral Inhibitor of Angiotensin-Converting Enzyme”, by MacGregor et al., BMJ, Vol. 2). Using a 0.01 significance level, is there sufficient evidence to support the claim that captopril has an effect on systolic blood pressure? i) Use the Wilcoxon signed-ranks test to conduct the required test without using "wilcox.test" function in R. Please state the hypothesis, provide the p-value, and the conclusion in the context of the problem. ii) Use the Wilcoxon signed-ranks test to conduct the required test using "wilcox.test" function in R. Please present a screenshot of the R output of your call to the function wilcox.test. iii) Would you recommend the Wilcoxon signed-ranks test over the…arrow_forward
- Algal blooms can have negative effects on an ecosystem by dominating its phytoplankton communities. Gonyostomum semen is a nuisance alga infesting many parts of northern Europe. Could the overall biomass of G. semen be controlled by grazing zooplankton species? A research team examined the relationship between the net growth rate of G. semen and the number of Daphnia magna grazers introduced in test tubes. Net growth rate was computed by comparing the initial and final abundances of G. semen in the experiment, with a negative value indicative of a decrease in abundance. The table contains the findings. Number of D. magna grazers Net growth rate of G. semen 1 2 3 4 -1.9 -2.5 -2.2 -3.9 5 -4.1 6 -4.3 Click to download the data in your preferred format. Excel Minitab 14-18 Minitab18+ JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! Software tells that the least-squares slope is b = -0.5286 with standard error SE, = 0.1059.arrow_forwardDuring the spring of 1999, many fuel storage facilities in Serbia were destroyed by bombing. As a result, significant quantities of oil products were spilled and burned,resulting in soil pollution. The article “Mobility of Heavy Metals Originating from Bombing of Industrial Sites” (B. Škrbić, J. Novaković, and N. Miljević, Journal of Environmental Science and Health, 2002:7–16) reports measurements of heavy metal concentrations at several industrial sites in June 1999, just after the bombing, and again in March of 2000. At the Smederevo site, on the banks of the Danube River, eight soil specimens taken in 1999 had an average lead concentration (in mg/kg) of 10.7 with a standard deviation of 3.3. Four specimens taken in 2000 had an average lead concentration of 33.8 with a standard deviation of 0.50. Find a 95% confidence interval for the increase in lead concentration between June 1999 and March 2000.arrow_forwardPlease help me with this problem and i needed only part d and e only please.... Very urgentarrow_forward
- The article "Application of Analysis of Variance to Wet Clutch Engagement" (M. Mansouri, M. Khonsari, et al., Proceedings of the Institution of Mechanical Engineers, 2002:117-125) presents the following fitted model for predicting clutch engagement time in seconds (y) from engagement starting speed in m/s (x1), maximum drive torque in N · m (x2), system inertia in kg · m² (x3), and applied force rate in kN/s (x4): y = -0.83 + 0.017.x, + 0.0895x, + 42.77.xz + 0.027x, – 0.0043x,x, The sum of squares for regression was SSR = 1.08613 and the sum of squares for error was SSE = 0.036310. There were 44 degrees of freedom for error. Predict the clutch engagement time when the starting speed is 20 m/s, the maximum drive torque is 17 N·m, the system inertia is 0.006 kg · m², and the applied force rate is 10 kN/s. b. Is it possible to predict the change in engagement time associated with an increase of 2 m/s in starting speed? If so, find the predicted change. If not, explain why not. Is it…arrow_forward4. Captopril is a drug designed to lower systolic blood pressure. When subjects were treated with this drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. Results are given in the accompanying table (based on data from “Essential Hypertension: Effect of an Oral Inhibitor of Angiotensin-Converting Enzyme”, by MacGregor et al., BMJ, Vol. 2). Using a 0.01 significance level, is there sufficient evidence to support the claim that captopril has an effect on systolic blood pressure? Explain why statistical methods from Z-interval, Z-test, T-interval or T-test –cannot be used for this problem. Then, use the sign test to conduct the required test in R studio. Please show your work.arrow_forward5.1 Byers and Williams (Viscosities of Binary and Ternary Mixtures of Polyaromatic Hydrocarbons," Journal of Chemical and Engineering Data, 32, 349 – 354, 1987) studied the impact of temperature (the regressor) on the viscosity (the response) of toluene- tetralin blends. The following table gives the data for blends with a 0.4 molar fraction of toluene. Temperature (°C) Viscosity (mPa·s) 24.9 1.133 35.0 0.9772 44.9 0.8532 55.1 0.7550 65.2 0.6723 75.2 0.6021 85.2 0.5420 95.2 0.5074 c. Basic principles of physical chemistry suggest that the viscosity is an exponential function of the temperature. Repeat part b using the appropriate transformation based on this information.arrow_forward
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