The accompanying data resulted from an experiment to study the nature of dependence of welding current on three factors: welding voltage, wire feed speed, and tip-to-workpiece distance. There were two levels of each factor (a 23 experiment) with two replications per combination of levels (the averages across replications agree with values given in the article “A Study on Prediction of Welding Current in Gas Metal Arc Welding,” J. Engr. Manuf., 1991: 64–69). The first two given numbers are for the treatment (1), the next two for a, and so on in standard order: 200.0, 204.2, 215.5, 219.5, 272.7, 276.9, 299.5, 302.7, 166.6, 172.6, 186.4, 192.0, 232.6, 240.8, 253.4, 261.6.
- a. Verify that the sums of squares are as given in the accompanying ANOVA table from Minitab.
- b. Which effects appear to be important, and why?
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Chapter 11 Solutions
Probability and Statistics for Engineering and the Sciences
- An article described an experiment in which observations on various characteristics were made using minichambers of three different types: (1) cooler (PVC frames covered with shade cloth), (2) control (PVC frames only), and (3) warmer (PVC frames covered with plastic). One of the article's authors kindly supplied the accompanying data on the difference between air and soil temperatures (°C). Cooler 1.59 1.43 1.88 1.26 1.91 1.86 1.90 1.57 1.79 1.72 2.41 2.34 0.94 1.34 1.76 Control 1.92 2.00 2.19 1.12 1.78 1.84 2.45 2.03 1.52 0.49 1.90 Warmer 2.57 2.60 1.93 1.58 2.30 0.84 2.65 0.15 2.74 2.53 2.13 2.86 2.31 1.91 (a) Compare measures of center for the three different samples. Cooler X = 1.76 Control X = 1.90 Warmer X = 2.305 (b) Calculate the standard deviations for the three different samples. (Round your answers to three decimal places.) Cooler S = 0.395 Control S = 0.522 Warmer S = 0.772 X x Interpret and compare the standard deviations for the three different samples.arrow_forwardAn article described an experiment in which observations on various characteristics were made using minichambers of three different types: (1) cooler (PVC frames covered with shade cloth), (2) control (PVC frames only), and (3) warmer (PVC frames covered with plastic). One of the article's authors kindly supplied the accompanying data on the difference between air and soil temperatures (°C). Cooler Control Warmer 1.59 1.92 2.57 1.43 2.00 2.60 1.88 2.19 1.93 1.26 1.12 1.58 1.91 1.78 2.30 1.86 1.84 0.84 1.90 2.45 2.65 1.57 2.03 0.12 1.79 1.52 2.74 1.72 0.58 2.53 2.41 1.90 2.13 2.34 2.86 0.96 2.31 1.34 1.91 1.76 (a) Compare measures of center for the three different samples. Cooler=_____________ Control=____________ Warmer=____________ (b) Calculate the standard deviations for the three different samples. (Round your answers to three decimal places.) Coolers=_______________ Controls=______________ Warmers=______________…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 Refrigeration on the Potassium Bitartrate Stability and Composition of Italian Wines" (A. Versari, D. Barbanti, et al., Italian Journal of Food Science, 2002:45- 52) reports a study in which eight types of white wine had their tartaric acid concentration (in g/L) measured both before and after a cold stabilization process. The results are presented in the following table: Wine Type Before After Difference 2.86 2.59 0.27 2.85 2.47 0.38 3 1.84 1.58 0.26 4 1.60 1.56 0.04 0.80 0.78 0.02 6. 0.89 0.66 0.23 2.03 1.87 0.16 1.90 1.71 0.19 Find a 95% confidence interval for the mean difference between the tartaric acid concentrations before and after the cold stabilization process.arrow_forward2. A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the table below (based on data from “Motorcycle Rider Conspicuity and Crash Related Injury: Case-Control Study”, by Wells et al., BMJ USA, Vol. 4). 1. Test the claim that injuries are independent of helmet color, using chisq.test function in R at a 0.05 significance level. Please state the hypothesis, present a screenshot of the R output for this test, and provide your conclusion in the context of the problem. 2. Should motorcycle drivers choose helmets with a particular color? If so, which color appears best? Provide your justification.arrow_forward
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