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ISU STAT 496 - Homework Assignment #3

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STAT 496, Spring 2003Homework Assignmen t #31. A paper products manufacturer is interested in improving the tensile strength of itspaper used in grocery bags. The current process uses 10% hardwood in the pulp,and at this level, the paper has an average tensile strength of approximately 15 psi.JMP analysis of the current process, control charts and capability analysis are givenon separate sheets.(a) Comment on the stability of the current process. Refer to the control charts onthe accompanying page.(b) Based on the control charts, what would be the estimate of the process standarddeviation?(c) Comment on the capability of the current process. Be sure to interpret anyappropriate capability indices. Indicate what the estimate of the process standarddeviation is. What proportion of paper would you expect to see below the lowerspecification of strength?2. The paper process engineers and operators suspect that tensile strength is a functionof hardwood concentration in the pulp. Specifically, they believe that higher hardwoodconcentrations would produce paper with higher tensile strengths. Because hardwoodis more expensive than the usual pulp wood, hardwood concentration must be 20% orlower. The experimen tal team decides to investigate four levels of hardwood concen-tration, 5%, 10%, 15%, and 20%. For each hardwood concentration, six test specimenswill be made using a pilot plant. All 24 specimens are tested for tensile strength bythe same technician using a single machine. The testing of the specimens is done inrandom order. Below are the resulting tensile strength measurements.Hardwood Concentration (%)51015207121519816192414 13 20 2212 17 18 23918161810 14 20 20(a) Comment on the use of control, randomization and replication in this experiment.(b) Construct a plot of the data. From the plot, does there appear to be a relationshipbetween hardwood concentration and tensile strength of the paper? If so, inwhich direction? Comment on the variation in tensile strength for each hardwoodconcentration.1(c) Code the hardwood concentration using the formula below. Calculate the simplelinear regression line relating tensile strength to coded hardwood concentration.C1i=2(Concentrationi− 12.5)5(d) Uncode your equation in (c) to obtain the simple linear regression relating tensilestrength to hardwood concentration. Graph this line on your plot in (b).(e) Predict the tensile strength of paper made with 17% hardwood.(f) What percentage of the variability in tensile strength is explained by the linearregression with hardwood concentration?(g) Is there a significant linear relationship bet ween tensile strength and hardwoodconcentration? How do you know? Caution: Be sure to use MSRepE rror(h) Add a quadratic term to you prediction equation by using the coded variable:C2i= C1i22−1512(i) What percentage of variability in tensile strength can be explained by the additionof this quadratic term?(j) Is the quadratic term statistically significant? How do you know? Caution: Besure to use MSRepE rror(k) Given the analysis above write a one paragraph summary about what you havelearned about the tensile strength of paper and the amount of hardwood used inits manufacture.You may use JMP or another computer program to verify what you have done above.• Use Graph - Overlay Plot to obtain a plot of the data.• Use Basic Stats - Distribution with Y, Columns - Tensile and By - Concentrationto obtain means and standard deviations for each hardwood concentration level.• Use Basic Stats - Fit Y by X to fit a simple linear regression of tensile strengthon coded hardwood concentration, C1i. You can also use this to fit a simple linearrelation of tensile strength on hardwood concentration directly. Note that informationon Lack of Fit is hidden so you need to click on the blue triangle to show this. WhatJMP calls Pure Error is Replication Error.• Use Modeling - Fit Model to fit a polynomial regression of tensile strength on C1iand C2i. Be sure to uncheck the Center Polynomial option in the Model Specificationpull down and choose the Minimal Report under


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