1. An aluminum master alloy manufacturer produces grain refiners in ingot form. The company produce: the product in four furnaces. Each furnace is known to have its own unique operating characteristics s any experiment run in the foundry that involves more than one furnace will consider furnaces as a nuisance variable. The process engineer suspect that stirring rate affects the grain size of the product. Each furnace can be run at four different stirring rate.A randomized block design is run for a particular refiner, and the resulting grain size data is as follows. Stirring Rate (rpm) F1 F2 F3 F4 5 8 4 5 6 10 14 5 6 9 15 14 6 9 2 20 17 9 3 6 a) Is there any evidence that stirring rate affects grain size? Graph the residuals from this experiment on a normal probability plot. Interpret the plot. c) Plot the residuals versus furnaces and stirring rate. Does this plot convey any useful information? d) What should the process engineers recommend concerning the choice of stirring rate and furnace for this particular grain refiner if small grain size is desirable?

1. An aluminum master alloy manufacturer produces grain refiners in ingot form. The company produce: the product in four furnaces. Each furnace is known to have its own unique operating characteristics s any experiment run in the foundry that involves more than one furnace will consider furnaces as a nuisance variable. The process engineer suspect that stirring rate affects the grain size of the product. Each furnace can be run at four different stirring rate.A randomized block design is run for a particular refiner, and the resulting grain size data is as follows. Stirring Rate (rpm) F1 F2 F3 F4 5 8 4 5 6 10 14 5 6 9 15 14 6 9 2 20 17 9 3 6 a) Is there any evidence that stirring rate affects grain size? Graph the residuals from this experiment on a normal probability plot. Interpret the plot. c) Plot the residuals versus furnaces and stirring rate. Does this plot convey any useful information? d) What should the process engineers recommend concerning the choice of stirring rate and furnace for this particular grain refiner if small grain size is desirable?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 5E: List the sample space of each experiment. Rolling one die and tossing one coin

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An aluminum master alloy manufacturer produces grain refiners in ingot form. The company produces the product in four furnaces. Each furnace is known to have its own unique operating characteristics, so any experiment run in the foundry that involves more than one furnace will consider furnaces as a nuisance variable. The process engineers suspect that stirring rate impacts the grain size of the product. Each furnace can be run at four different stirring rates. A randomized block design is run for a particular refiner and the resulting grain size data is as follows. Furnace Stirring Rate 1 2 3 4 5 8 4 5 6 10 14 5 6 9 15 14 6 9 2 20 17 9 3 6 (a) Is there any evidence that stirring rate impacts grain size? Conduct hypothesis testing to answer this question. (b) Graph the residuals from this experiment on a normal probability plot. Interpret this plot.
An aluminum master alloy manufacturer produces grain refiners in an ingot form. The company produces the product in four furnaces. Each furnace is known to have its own unique operating characteristics, so any experiment runs in the foundry that involves more than one furnace will consider furnaces as a nuisance variable. The process engineers suspect that the stirring rate affects the grain size of the product. Each furnace can be run at four different stirring rates. A randomized block design is run for a particular refiner, and the resulting grain size data are as follows. Stirring rate Furnace grain size 5 1 8 10 1 14 15 1 14 20 1 17 5 2 4 10 2 5 15 2 6 20 2 9 5 3 5 10 3 6 15 3 9 20 3 3 5 4 6 10 4 9 15 4 2 20 4 6 1) Does the stirring rate affects grain size? 2) Analyze the residuals from the experiment. Are all assumptions satisfied?
The chemical benzene is highly toxic to humans. However, it is used in the manufacture of many medicine dyes, leather, and coverings. Government regulations dictate that for any production process involving benzene, the water in the output of the process must not exceed 7,950 parts per million (ppm) of benzene. For a particular process of concern, the water sample was collected by a manufacturer 25 times randomly and the sample average x was 7960 ppm. It is known from historical data that the standard deviation o is 100 ppm. (a) What is the probability that the sample average in this experiment would exceed the government limit if the population mean is equal to the limit? (b) Is an observed x = 7960 in this experiment a firm evidence that the population mean for the process exceeds the government limit? Assume that the distribution of benzene concentration is normal.
An aluminum master alloy manufacturer produces grain refiners in ingot form. The company produces the product in four furnaces. Each furnace is known to have its own unique operating characteristics, so any experiment run in the foundry that involves more than one furnace will consider furnaces as a nuisance variable. The process engineers suspect that stirring rate impacts the grain size of the product. Each furnace can be run at four different stirring rates. A randomized block design is run for a particular refiner and the resulting grain size data is as follows. Furnace Stirring Rate 1 2 3 4 5 8 4 5 6 10 14 5 6 9 15 14 6 9 2 20 17 9 3 6 (a) Plot the residuals versus furnace and stirring rate. Does this plot convey any useful information? (b) What should the process engineers recommend concerning the choice of stirring rate and furnace for this particular grain refiner if small grain size is desirable?
Benzene is a pollutant that, according to studies, can be associated with health problems. Benzene is found in air, water, and soil and comes from both industrial and natural sources. Benzene levels in indoor air are generally higher than outdoors. The main source of benzene in indoor air appears to be tobacco smoke, thus the combustion of tobacco is a major source of pollution. Benzene levels are measured in a random sample of 36 bars in a city, obtaining an average benzene level of 19.2 mg / m3, with a standard deviation of 2.1 mg / m3. Estimate the mean benzene level in bars in this city using a 95% confidence interval. (do your calculations to 4 decimal places) (need the process can be by hand ,Excel or R.) a)Other solution b)[18.48946, 19.91054] c)[19.0950, 19.3050] d)[18.5140, 19.8859] e)[18.6243, 19.7757] f)[18.4315, 19.7936]
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A study is conducted to measure the difference between three teaching methods which are blended leaming (Method A), open and distance learning (Method B) and face-to-face leaming (Method C). A random sample of 21 students was participated in the study. Seven students were randomly assigned to each teaching method on STA210 course. A test was administered at the end of the course and the scores obtained by the students are recorded below. Method A Method B Method C 23 19 26 24 23 24 19 18 21 26 24 29 22 20 28 23 25 22 24 19 28 a) At 5% significance level, test whether there are significant differences between the mean test scores for the three teaching methods. b) Construct a 95% confidence interval for the mean difference of test score between face to face and open distance learning. Can we conclude that the mean test score of face- to-face learning exceeds open and distance leaming?