STAT 411设计实验

用于解决每个问题的所有代码，以及RELEVANT输出。您可以将其包括在内作为报告正文的一部分，或者（最好）可以将所有代码放在报告的附录中。做不要包含错误的代码或错误消息，除非它们与您在讨论所有代码/输出必须采用单空格字体（非比例）；
手写或打字的数学推导或证明（如果需要）；你在回答问题时使用的任何图表。查看R的帮助设施或前往现场存R中的图形的信息可纳入您的报告；对作业中提出的每个问题的结论进行书面描述。工作分配概述该分配有12个问题，其中1个额外的STAT 616仅存在问题。STAT 411Homework 3 – Design of Experiments

1.Rules

The report for the assignment should be in a single .pdf file, uploaded to Canvas with hard copy to the TAat or before the due date and time. Your report must include:A cover page with name, class, assignment number, and date;All of the code you used to solve each problem, along with RELEVANT output. You can include thisas part of the body of the report, or (preferably) you can put all of the code in an appendix of the report. Donot include incorrect code or error messages, unless they are related to some point you are raising in yourdiscussion. All code/output must be in a monospace font (not proportional);Handwritten or typed mathematic derivations or proofs if needed;Any graphs that you used in answering the question. See R's help facility or go to thesitehttps://statistics.berkeley.edu/computing/saving-plots-r for information on saving graphs from R in a formthat can be incorporated into your report;A written description of your conclusion for each question asked in the assignment.

2.Assignment overview

This assignment has 12 problems with 1 additional STAT 616-only problem.STAT 411 Students choose 6 of these problems and solve.STAT 616 Student choose 8 of these problems plus the 616 only problem.STAT 411/616 Homework of 41. A series of runs were performed to determine how the wash water temperature and the detergentconcentration affect the bacterial count on the palms of subjects in a hand washing experiment.a. Identify the experimental unit.b. Identify the factors.c. Identify the response.2. Explain the difference between an experimental unit and a sub-sample or sub-unit in relation to theexperiments described in l.3. Explain the difference between a sub-sample and a duplicate in relation to the experiment described in1.4. Describe a situation within your realm of experience (your work, your hobby, or school) where youmight like to predict the result of some future action. Explain how an experimental design,
Page 3 of 46. Paint used for marking lanes on a highway must be very durable. In one trial paint from fourdifferrence suppliers, labeled GS, FD, L and ZK, were tested on six different highway sites, denoted1,2,3,4,5,6. After considerable lenght of time, which included different levels of traffic and weather, theaverage wear for the samples at the six sites was as follows:The objective was to compare the wear of the paints from the different suppliers.a. What kind of an experimental design is this.b. Make an ANOVA.c. Obtain confidence limits for the supplier averages.d. Make checks that might indicate departures from assumptions.e. Do you think these data contain bad values?f. What can you say about the relative resistance to wear of the four paints~g. Do you think this experimental arrangement was helpful?7. Consider planning an experiment to determine how the flavor duration of gum is affected by thecharacteristics of the gum such as Factor A (type of gum stick or tablet), Factor B (flavor of gum), andFactor C (regular or sugar-free), see Rogness and Richardson (2003).a. If several subjects were recruited to participate in the study and each was asked to chew andrecord the flavor duration (in minutes) of one or more types of gum, what would theexperimental unit be?b. How could experimental units be blocked to reduce the variance of experimental error andincrease the power for detecting differences?c. Choose at least two of the factors listed above and provide a randomized list for an RCB design8. Lew (2007) presents the data from an experiment to determine whether cultured cells respond to twodrugs. The experiment was conducted using a stable cell line plated onto Petri dishes, with eachexperimental run involving assays of responses in three Petri dishes: one treated with drug 1, onetreated with drug 2, and one untreated serving as a control. The data are shown in the table below:STAT 411/616 Homework 3 Page 4 of 4a. Analyze the data as if it came from a completely randomized design using the modelij i ijy μ τ ε= + + . Is there a significant difference between the treatment groups?b. Analyze the data as an RCB design, where experiment number represents a blocking factor.c. Is there any difference in the results you obtain in (a) and (b)? If so explain what may be thecause of the difference in the results and which method would you recommend?9. Consider a 28-4 fractional factorial design. Answer the following questions:a. How many factors does this design have.b. How many runs are involved in this design.c. How many levels for each factor.d. How many independent generators are there for this design.10. Repeat problem 9. for a 26-1 design11. Melo et al. (2007) used a 24-1 factional factorial design with generator D = ABC to study the factors thatinfluence the production of levan by aerobic fermentation using the yeast Zymomonas mobilis. Levanis a sugar polymer of the fructan group, which has been shown to have anti-tumor activity againstsarcoma and Ehrlich carcinoma in Swiss albino mice. The factors varied in the fermentation mediumand their levels are shown in the table below.a. What is the defining relation and complete alias structure for this design?b. What is the resolution of this design?c. The fermentations were carried out batchwise in Pyrex flasks. After 72 hours of fermentation,the levan produced was extracted from the fermented medium and its dry weight wasdetermined. The results (in g.L-1) for the eight experiments (in standard order) were: 4.70, 14.67,1.71, 3.73, 9.47, 7.61, 0.15, 4.78. From this data, calculate the seven effects and make anormalprobability plot to determine what is significant.d. Delete thesmallest three effects and fit the model again. Are the four effectsleft in the modelsignificant?e. Based on the effect heredity principle, what do you think the significant string of aliased two-factor interactions could represent?f. Can the design be collapsed to a full factorial by ignoring insignificant factors?g. Based on what you said in (e) write an interpretation of the significant effects and interaction.Based on your model determine the factor levels that will produce the maximum dry weight oflevan.12. Create a central composite design (CCD) for two factors using R's rsm package.a. Create the uniform precision CCD and store the design along with random numbers (simulatedresponse) in a data frame.b. Use the Vdgraph package to make a variance dispersion graph or a fraction of design spaceplot of the design you created.c. Repeat (a) through (b) for a face-centered cube design (i.e., CCD with axial points at ±1).d. Based on the graphs you made, which design do you prefer? State the
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