공업통계학 principles of statistics for engineers and scientists 연습문제 풀이 - 졸업논문

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설명 : 공업통계학 principles of statistics for engineers and scientists 7.1 7.2 7.3 7.4 8.1 8.2 8.3장 연습문제 풀이 7.1 6. A sample of 45 room air conditioners of a certain model had a mean sound pressure of 52 decibels (dB) and a standard deviation of 5 dB, and a sample of 60 air conditioners of a different model had a mean sound pressure of 46 dB and a standard deviation of 2 dB. Find a 98% confidence interval for the difference in mean sound pressure between the two models. 11. Two corrosion inhibitors, one more expensive than the other are being considered for treating stainless steel. To compare them, specimens of stainless steel were immersed for four hours in a solution containing sulfuric acid and corrosion inhibitor. Thirty-eight specimens immersed in the less expensive product had an average weight loss of 242 mg and a standard deviation of 20 mg, and 42 specimens immersed in the more expensive product had an average weight loss of 180 mg and a standard deviation of 31 mg. It is determined that the more expensive product will be used if it can be shown that its additional mean weight loss over that of the less expensive method is greater than 50 mg. Perform an appropriate hypothesis test, and on the basis of the results, determine which inhibitor to use. 7.2 4. The article "Occurrence and Distribution of Ammonium in Iowa Groundwater" (K. Schilling, Water Environment Research, 2002:177-186) describes measurements of ammonium concentrations (in mg/L) at a large number of wells in the state of Iowa. These included 349 alluvial wells and 143 quaternary wells. Of the alluvial wells, 182 had concentrations above 0.1, and 112 of the quaternary wells had concentrations above 0.1. Find a 95% confidence interval for the difference between the proportions of the two types of wells with concentrations above 0.1. 9. Two extrusion machines that manufacture steel rods are being compared. In a sample of 1000 rods taken from machine 1, 960 met specifications regarding length and diameter. In a sample of 600 rods taken from machine 2, 582 met the specifications. Machine 2 is more expensive to run, so it is decided that machine 1 will be used unless it can be convincingly shown that machine 2 produces a larger proportion of rods meeting specifications. 7.3 9. A computer scientist is studying the tendency for a computers running a certain operating system to run more slowly as the operating system ages. She measures the time (in seconds) for a certain application to load for nine computers one month after installation and for seven computers six months after installation. The results are as follows: 13. The article "Permeability, Diffusion and Solubility of Gases" (B. Flaconnéche, et al., Oil and Gas Science and Technology, 2001:262-278) reported on a study of the effect of temperature and other factors on gas transport coefficients in semicrystalline polymers. The permeability coefficient (in )of was measured for extruded medium-density polyethelene at both and .The results are as follows: 7.4 3. The water content (in percent) for 7 bricks was measured shortly after manufacture, then again after the bricks were dried in a furnace. The results were as follows. 10. The article "Modeling of Urban Area Stop-and-Go Traffic Noise" (P. Pamanikabud and C. Tharasawatipipat, Journal of Transportation Engineering, 1999:152-159) presents measurements of traffic noise, in dBA, from 10 locations in Bangkok, Thailand. Measurements, presented in the following table, were made at each location, in both the acceleration and deceleration lanes. 8.1 1. A chemical reaction is run 12times, and the temperature (in )and the yield (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: 9. In a study to determine the relationship between ambient outdoor temperature and the rate of evaporation of water from soil, measurements of average daytime temperature in and evaporation in mm/day were taken for 40 days. The results are shown in the following table. 8.2 3. The article "Application of Genetic Algorithms to Optimum Design of Elasto-damping Elements of a Half-Car Model Under Random Road Excitations" (M. Mirzael and R. Hassannejad, Proceedings of the Institution of Mechanical Engineers, 2007:515-526) presents values of a coefficient (y), a unitless quantity that measures the road impact on an automobile suspension, and the time (t) for the car to travel a distance equal to the length between the front and rear axles. The results are as follows: 8.3 1. In an experiment to determine the factors affecting tensile strength in steel plates, the tensile strength (in ), the manganese content (in parts per thousand), and the thickness (in mm) were measured for a sample of 20 plates. The following MINITAB output presents the results of fitting the model Tensile strength = Manganese + Thickness. 3. The data used to fit the model in Exercise 1 are presented in the following table, along with the residuals and the fitted values. Plot the residuals versus the fitted values. Does the plot indicate that the linear model is reasonable? Explain.

공업통계학 principles of statistics for engineers and scientists 7.1 7.2 7.3 7.4 8.1 8.2 8.3장 연습문제 풀이 7.1 6. A sample of 45 room air conditioners of a certain model had a mean sound pressure of 52 decibels (dB) and a standard deviation of 5 dB, and a sample of 60 air conditioners of a different model had a mean sound pressure of 46 dB and a standard deviation of 2 dB. Find a 98% confidence interval for the difference in mean sound pressure between the two models. 11. Two corrosion inhibitors, one more expensive than the other are being considered for treating stainless steel. To compare them, specimens of stainless steel were immersed for four hours in a solution containing sulfuric acid and corrosion inhibitor. Thirty-eight specimens immersed in the less expensive product had an average weight loss of 242 mg and a standard deviation of 20 mg, and 42 specimens immersed in the more expensive product had an average weight loss of 180 mg and a standard deviation of 31 mg. It is determined that the more expensive product will be used if it can be shown that its additional mean weight loss over that of the less expensive method is greater than 50 mg. Perform an appropriate hypothesis test, and on the basis of the results, determine which inhibitor to use. 7.2 4. The article "Occurrence and Distribution of Ammonium in Iowa Groundwater" (K. Schilling, Water Environment Research, 2002:177-186) describes measurements of ammonium concentrations (in mg/L) at a large number of wells in the state of Iowa. These included 349 alluvial wells and 143 quaternary wells. Of the alluvial wells, 182 had concentrations above 0.1, and 112 of the quaternary wells had concentrations above 0.1. Find a 95% confidence interval for the difference between the proportions of the two types of wells with concentrations above 0.1. 9. Two extrusion machines that manufacture steel rods are being compared. In a sample of 1000 rods taken from machine 1, 960 met specifications regarding length and diameter. In a sample of 600 rods taken from machine 2, 582 met the specifications. Machine 2 is more expensive to run, so it is decided that machine 1 will be used unless it can be convincingly shown that machine 2 produces a larger proportion of rods meeting specifications. 7.3 9. A computer scientist is studying the tendency for a computers running a certain operating system to run more slowly as the operating system ages. She measures the time (in seconds) for a certain application to load for nine computers one month after installation and for seven computers six months after installation. The results are as follows: 13. The article "Permeability, Diffusion and Solubility of Gases" (B. Flaconnéche, et al., Oil and Gas Science and Technology, 2001:262-278) reported on a study of the effect of temperature and other factors on gas transport coefficients in semicrystalline polymers. The permeability coefficient (in )of was measured for extruded medium-density polyethelene at both and .The results are as follows: 7.4 3. The water content (in percent) for 7 bricks was measured shortly after manufacture, then again after the bricks were dried in a furnace. The results were as follows. 10. The article "Modeling of Urban Area Stop-and-Go Traffic Noise" (P. Pamanikabud and C. Tharasawatipipat, Journal of Transportation Engineering, 1999:152-159) presents measurements of traffic noise, in dBA, from 10 locations in Bangkok, Thailand. Measurements, presented in the following table, were made at each location, in both the acceleration and deceleration lanes. 8.1 1. A chemical reaction is run 12times, and the temperature (in )and the yield (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: 9. In a study to determine the relationship between ambient outdoor temperature and the rate of evaporation of water from soil, measurements of average daytime temperature in and evaporation in mm/day were taken for 40 days. The results are shown in the following table. 8.2 3. The article "Application of Genetic Algorithms to Optimum Design of Elasto-damping Elements of a Half-Car Model Under Random Road Excitations" (M. Mirzael and R. Hassannejad, Proceedings of the Institution of Mechanical Engineers, 2007:515-526) presents values of a coefficient (y), a unitless quantity that measures the road impact on an automobile suspension, and the time (t) for the car to travel a distance equal to the length between the front and rear axles. The results are as follows: 8.3 1. In an experiment to determine the factors affecting tensile strength in steel plates, the tensile strength (in ), the manganese content (in parts per thousand), and the thickness (in mm) were measured for a sample of 20 plates. The following MINITAB output presents the results of fitting the model Tensile strength = Manganese + Thickness. 3. The data used to fit the model in Exercise 1 are presented in the following table, along with the residuals and the fitted values. Plot the residuals versus the fitted values. Does the plot indicate that the linear model is reasonable? Explain.

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