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ISU STAT 496 - exam1 -S01

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Statistics 496, Applied Statistics for Industry II Name:Exam 1, Spring 2001 Site:INSTRUCTIONS: You will have 1 hour and 30 minutes to complete the exam. There are 6questions worth a total of 100 points. Not all questions have the same point value so gauge yourtime appropriately. Read the questions carefully and completely. Answer each question and showwork in the space provided on the exam. Turn in the entire exam when you are done or whentime is up. For essay questions, think before you write.1. [8 pts] Engineers monitor the outside diameter of a motor shaft that is machined on a CNCturning center. Subgroups of 5 consecutive parts are selected approximately every half hour.There are a total of 35 such subgroups. Subgroup statistics, such as the mean, range andstandard deviation are calculated.(a) [4] Using the average range,R=16.97 and the average standard deviation, s=6.85 cal-culate two separate estimates of the process standard deviation, σ.(b) [4] If the standard deviation of all 175 individual measurements is s=10.32, what doesthis tell you about the stability of the process?2. [22 pts] In a 1995 article in Journal of Applied Polymer Science the authors (Sutter, Jobeand Crane) reported on polymer resin weight loss at high temperatures. The larger the weightloss in a polymer resin at a particular time/temperature combination the more unstable, andthus less desirable, the polymer resin. Specimens of five polymer resins (Avimid-N, VCAP-75,N-CYCAP, PRMR-II-50 and AFR700B) are to be exposed for 400 hours to 371oC.(a) [3] We wish to be able to detect a difference as small as 2 standard deviations with a10% chance of missing a real difference of that size and a 5% chance of falsely detectinga difference. How many specimens of each polymer would we need?(b) [3] Our budget allows for 4 specimens of each of the five polymers. Give a combinationof ALPHA, BETA and ∆/σ that will fit our budget.1(c) [4] The data are plotted below. Comment on the differences (level and spread) amongthe resins in terms of weight loss.(d) [4] Below are the data and the associated ANOVA table. Compute the LSD (use t=2).Avimid-N VCAP-75 N-CYCAP PMR-II-50 AFR700B10.66 25.88 25.23 27.52 28.439.10 23.59 25.37 29.14 28.959.09 26.51 24.59 29.89 24.7910.23 30.54 25.57 28.57 24.83Mean 9.77 26.63 25.19 28.78 26.75Source df Sum of Squares Mean SquarePolymer 4 958.31 239.58Error 15 45.75 3.05Total 19 1004.06(e) [5] Using the LSD calculated in (d), which of the resins show statistically significantdifferences in mean weight loss?2(f) [3] Which polymer, if any, would you recommend? Explain briefly your choice.3. [12 pts] The three fundamental principles of a designed experiment are: control of outsidevariables, randomization and replication. Does the following scenario adhere to the threeprinciples? If so, describe how. If not, indicate how you would change the design to incorpo-rate the missing principle(s). Be specific and be sure to comment on each principle.An experiment is to be performed on the effect of drill speed on the size of drilled holes.A single 0.25 inch drill bit in a vertical head milling machine will be used for the experiment.All drilling will be done by the same operator. A single bar of 6061 Aluminum will be used.Four speeds will be investigated: 100, 150, 200 and 250 rpms. The operator will pick a speedat random from the four and will drill 20 holes. The process will be repeated, picking aspeed at random from those remaining and drilling 20 holes until all 4 speeds have been used.Each of the holes will be measured using a special caliper. The order of measurement will berandom.34. [16 pts] An independent research firm wishes to study the effects of the speed of an automobileand emission levels. The experiment will be run on a dynamometer rather than on a test trackso that factors such as wind, road conditions and driver will not affect the results. Ideallynine speeds (miles per hour) will be used: 40, 45, 50, 55, 60, 65, 70, 75, 80.(a) [3] The firm wishes to be able to detect a difference of 2 standard deviations. It canaccept a 10% chance of missing such a difference when one exists, but wants only a 5%chance of declaring a difference significant when there is no difference. What is the totalnumber of experimental units necessary for the experiment?(b) [3] When the experiment is proposed there are enough resources for 7 experimental unitsfor each of the nine speeds. Can one design an experiment that is able to detect a 2standard deviation difference? If so, what compromises must be made? Be specific.(c) [4] Budget cuts at the firm limit the total number of experimental units to 45. Can anexperiment be conducted that meets the requirements in (a)? Explain briefly. Hint: Itis okay to reduce the scope of the experiment.(d) [6] The firm has to decide whether to use one car, repeating the measurement process 45times, or 45 cars, same make, model, engine capacity, equipment, etc., in the experiment.Comment on each of these choices. Which do you think is better? Why?45. [27 pts] An aluminum smelting operation makes its own carbon anodes for use in theiraluminum smelting pots. The baked density of the anode is an important quality characteristicbecause it affects the usable life of the anode. An experiment is conducted to see the effect ofbake temperature on anode density. Twenty anodes are made using the same raw materials,methods and people. Anodes are assigned at random to one of four temperatures, 500, 525,550 and 575oC. The temperatures are run in a random order and the density measurementsfor all 20 anodes are done at random.(a) [6] Discuss how the three fundamental principles of experimentation are incorporatedinto this experiment.The data on anode density after baking are summarized and plotted below.Temperature Number Mean,YiVariance, s2i500 5 41.70 0.025525 5 41.56 0.043550 5 41.28 0.037575 5 40.72 0.037Average Variance = 0.03555(b) [3] Describe the relationship between bake temperature and density of the anodes.5(c) [8] Give the simple linear regression equation of density on temperature. Hint: It willbe easiest to use a coded temperature, C1, to find the regression of density on C1andthen convert.(d) [5] Is the linear relationship statistically significant? How do you know?(e) [2] Use the linear regression equation to predict the density of anodes baked at 510oC.(f) [3] The slope coefficient for the quadratic term is ˆm2= −0.105 and its associated sumof squares is 0.2205. Is the


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