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ISU STAT 496 - Exam 2

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Statistics 496, Applied Statistics for Industry II Name:Exam 2, Spring 2001 Site:INSTRUCTIONS: You will have 1 hour and 30 minutes to complete the exam. There are 4questions 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. [35 pts] An automobile assembly plant uses an automated fixture to center a glove boxdoor to the instrument panel. In order to improve door parallelism during assembly a 24experiment with a single replicate is performed. The response is door parallelism in mm.Below are the factors, estimated full effects, and sums of squares for each estimated effect.Factor Low (−)High(+)A: RH cowl fore/aft movement Nominal 5 mmB: Center brace attachment sequence Before AfterC: Plenum gasket No YesD: Evaporator case setup, fore/aft Nominal 5 mmTrmt. Estimated EffectComb. A B C D Effect Name SSEffect1 −−−− −0.0875 Mean —–a+ −−− −0.6550 A 1.716b − + −− 0.7975 B 2.544ab + + −− 0.1475 AB 0.087c −−+ − 0.6375 C 1.626ac + − + −−0.1175 AC 0.055bc − ++−−0.1900 BC 0.144abc+++− 0.1750 ABC 0.123d −−−+ 0.3225 D 0.416ad + −−+ −0.0325 AD 0.004bd − + − + −0.1550 BD 0.096abd + + − + 0.1000 ABD 0.040cd −−+ + 0.0100 CD 0.000acd + − ++−0.1400 ACD 0.078bcd − +++−0.1075 BCD 0.046abcd++++ 0.1225 ABCD 0.0601(a) [5] Below is a main effects plot. Describe the effect on parallelism for each of the fourfactors in the experiment.(b) [4] Below is an interaction plot for plenum gasket and evaporator case set up. Whatdoes this plot tell you about interaction between these two variables? Be sure to mentionwhat you see in the plot that supports your answer.2(c) [4] On the normal plot of estimated full effects identify and label those effects thatappear to be significant.(d) [8] Using one of the methods discussed in class, come up with an estimate of errorvariability, and a standard error of an estimated full effect.(e) [4] Which effect(s) is(are) statistically significant?(f) [4] Give a prediction equation using only those effects that are statistically significant.(g) [6] Using your equation in (f), give a predicted value and prediction interval (use t=2)for the glove box door parallelism where the RH cowl fore/aft movement is nominal, thecenter brace is attached after, there is no plenum gasket and the evaporator case setup,fore/aft is nominal.32. [25 pts] An experiment is performed to determine if there is any difference in mean hardnessreadings for four types of tips used on a hardness tester. Five test coupons from a particulartype of alloy are used as blocks and each tip is tested once on each coupon. The testing isnon-destructive so that coupons can be tested several times. The data from the experimentare summarized below:Type of Tip1234number 5555mean hardness 9.4 9.5 9.3 9.8Source df Sum of SquaresRep Error 16 1.76Blocks 4 1.52(a) [5] For a randomized complete block design explain explicitly how you would randomizethe runs. Be sure to state how many runs there are.(b) [4] What size difference in mean hardness readings will you be able to detect withα =0.10 and β =0.10?(c) [6] If we ignore blocking (this is the wrong analysis but do it anyway), compute the LSD(use t=3) for comparing the types of tips. Which tips are significantly different?4(d) [6] If we incorporate blocking (as we should) in our analysis, compute the LSD (againuse t=3) for comparing the types of tips. Which tips are significantly different?(e) [4] What do parts (c) and (d) indicate about paying attention to how the data arecollected when it comes to data analysis?3. [10 pts] The three basic principles of sound experimental design are control of outside vari-ables, randomization and replication. Failing to include any one of these principles will resultin difficulties with the analysis of the resulting data.(a) [4] What difficulties are encountered if one fails to replicate?(b) [6] What difficulties are encountered if one fails to control outside variables? How doesrandomization help with these difficulties?54. [30 pts] An experiment is conducted on the silencing ability of a filter added to the exhaustsystem of a vehicle. Three factors are investigated, each at two levels (the data are givenbelow in standard Yates order). There are two replicates for each treatment combination.The response is the noise level reading in decibels. One objective of the experiment is toverify that the type of filter has no affect on the noise level.A: Vehicle B: Filter C: Side Noise Mean Var.Size Type Monitored LevelYs2small(−1) standard(−1) right(−1) 810, 820 815 50large(+1) standard(−1) right(−1) 780, 790 785 50small(−1) Octel(+1) right(−1) 820, 820 820 0large(+1) Octel(+1) right(−1) 775, 775 775 0small(−1) standard(−1) left(+1) 835, 835 835 0large(+1) standard(−1) left(+1) 760, 770 765 50small(−1) Octel(+1) left(+1) 825, 825 825 0large(+1) Octel(+1) left(+1) 770, 760 765 50(a) [5] For a completely randomized design, explain explicitly how you would randomize theruns. Be sure to indicate how many runs there are.(b) [3] What is the MSrepE rrorfor this experiment?(c) [6] Complete the following table of estimated full effects.Effect Estimated Effect EstimatedName Full Effect Name Full EffectMean C −1.25A −51.25 AC −13.75B −3.75 BCAB −1.25 ABC 6.256(d) [6] Which effects are statistically significant? Be sure to give the critical effect size usingt=3. According to this analysis, does the type of filter make a difference in terms ofaverage noise level?(e) [4] Using a prediction equation containing only significant terms, what would you rec-ommend for the vehicle size, filter type and monitoring side to produce the lowest noiselevel?(f) [6] Give the predicted noise level and prediction interval (use t=2) for your recommen-dation in


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ISU STAT 496 - Exam 2

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