Solution Manual for Design and Analysis of Experiments, 10th Edition

Solution Manual for Design and Analysis of Experiments, 10th Edition Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY 1-1 Chapter 1 Introduction Solutions 1.1S. Suppose that you want to design an experiment to study the proportion of unpopped kernels of popcorn. Complete steps 1-3 of the guidelines for designing experiments in Section 1.4. Are there any major sources of variation that would be difficult to control? Step 1 – Recognition of and statement of the problem. Possible problem statement would be – find the best combination of inputs that maximizes yield on popcorn – minimize unpopped kernels. Step 2 – Selection of the response variable. Possible responses are number of unpopped kernels per 100 kernals in experiment, weight of unpopped kernels versus the total weight of kernels cooked. Step 3 – Choice of factors, levels and range. Possible factors and levels are brand of popcorn (levels: cheap, expensive), age of popcorn (levels: fresh, old), type of cooking method (levels: stovetop, microwave), temperature (levels: 150C, 250C), cooking time (levels: 3 minutes, 5 minutes), amount of cooking oil (levels, 1 oz, 3 oz), etc. 1.2. Suppose that you want to investigate the factors that potentially affect cooked rice. (a) What would you use as a response variable in this experiment? How would you measure the response? (b) List all of the potential sources of variability that could impact the response. (c) Complete the first three steps of the guidelines for designing experiments in Section 1.4. Step 1 – Recognition of and statement of the problem. Step 2 – Selection of the response variable. Step 3 – Choice of factors, levels and range. 1.3. Suppose that you want to compare the growth of garden flowers with different conditions of sunlight, water, fertilizer and soil conditions. Complete steps 1-3 of the guidelines for designing experiments in Section 1.4. Step 1 – Recognition of and statement of the problem. Step 2 – Selection of the response variable. Step 3 – Choice of factors, levels and range. 1.4. Select an experiment of interest to you. Complete steps 1-3 of the guidelines for designing experiments in Section 1.4. Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY 1-2 1.5. Search the World Wide Web for information about Sir Ronald A. Fisher and his work on experimental design in agricultural science at the Rothamsted Experimental Station. Sample searches could include the following: 1.6. Find a Web Site for a business that you are interested in. Develop a list of factors that you would use in an experimental design to improve the effectiveness of this Web Site. 1.7. Almost everyone is concerned about the rising price of gasoline. Construct a cause and effect diagram identifying the factors that potentially influence the gasoline mileage that you get in your car. How would you go about conducting an experiment to determine any of these factors actually affect your gasoline mileage? 1.8. What is replication? Why do we need replication in an experiment? Present an example that illustrates the differences between replication and repeated measures. Repetition of the experimental runs. Replication enables the experimenter to estimate the experimental error, and provides more precise estimate of the mean for the response variable. 1.9S. Why is randomization important in an experiment? To assure the observations, or errors, are independently distributed randome variables as required by statistical methods. Also, to “average out” the effects of extraneous factors that might occur while running the experiment. 1.10S. What are the potential risks of a single, large, comprehensive experiment in contrast to a sequential approach? The important factors and levels are not always known at the beginning of the experimental process. Even new response variables might be discovered during the exp