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Question: Three catalysts are used in a chemical

Three catalysts are used in a chemical process; a control (no catalyst) is also included. The following are yield data from the process:
Three catalysts are used in a chemical process; a control (no catalyst) is also included. The following are yield data from the process: 


Use Dunnett’s test at the α = 0.01 level of significance to determine if a significantly higher yield is obtained with the catalysts than with no catalyst.

Use Dunnett’s test at the α = 0.01 level of significance to determine if a significantly higher yield is obtained with the catalysts than with no catalyst.





Transcribed Image Text:

Catalyst Control 1 2 3 74.5 77.5 81.5 78.1 76.1 82.0 82.3 80.2 75.9 80.6 81.4 81.5 78.1 84.9 79.5 83.0 76.2 81.0 83.0 82.1


> In the study An X-Ray Fluorescence Method for Analyzing Polybutadiene-Acrylic Acid (PBAA) Propellants (Quarterly Reports, RK-TR-62-1, Army Ordnance Missile Command), an experiment was conducted to determine whether or not there was a significant differen

> A 22 factorial experiment is analyzed by the Statistics Consulting Center at Virginia Tech. The client is a member of the Department of Housing, Interior Design, and Resource Management. The client is interested in comparing cold start to preheating oven

> A large petroleum company in the Southwest regularly conducts experiments to test additives to drilling fluids. Plastic viscosity is a rheological measure reflecting the thickness of the fluid. Various polymers are added to the fluid to increase viscosit

> Use the runs test to test, at level 0.01, whether there is a difference in the average operating time for the two calculators of Exercise 16.17 on page 670. Exercise 16.17: The following data represent the number of hours that two different types of sci

> A preliminary experiment is conducted to study the effects of four factors and their interactions on the output of a certain machining operation. Two runs are made at each of the treatment combinations in order to supply a measure of pure experimental er

> A Plackett-Burman design was used to study the rheological properties of high-molecular-weight copolymers. Two levels of each of six variables were fixed in the experiment. The viscosity of the polymer is the response. The data were analyzed by the Stati

> Construct a Plackett-Burman design for 10 variables containing 24 experimental runs.

> Consider the 1/16 of the 27 factorial discussed in Section 15.9. List the additional 11 defining contrasts.

> A 25 factorial plan is used to build a regression model containing first-order coefficients and model terms for all two-factor interactions. Duplicate runs are made for each factor. Outline the analysis-of-variance table, showing degrees of freedom for r

> Use the coal cleansing data of Exercise 15.2 on page 609 to fit a model of the type E(Y ) = β0 + β1x1 + β2x2 + β3x3, where the levels are x1, percent solids: 8, 12 x2, flow rate: 150, 250 gal/min x3, pH:

> In Case Study 15.2 involving the coal cleansing data, the percent solids in the process system is known to vary uncontrollably during the process and is viewed as a noise factor with mean 0 and varianceσ2z . The response, cleansing efficiency,

> Consider Case Study 15.1 involving the injection molding data. Suppose mold temperature is difficult to control and thus it can be assumed that in the process it follows a normal distribution with mean 0 and variance σ2z. Of concern is the var

> Consider the following 23 factorial with control variables x1 and x2 and noise variable z. Can x1 and x2 be chosen at levels for which Var(y) is minimized? Explain why or why not.

> Consider an example in which there are two control variables x1 and x2 and a single noise variable z. The goal is to determine the levels of x1 and x2 that are robust to changes in z, i.e., levels of x1 and x2 that minimize the variance produced in the r

> A silver-plating process is used to coat a certain type of serving tray. When the process is in control, the thickness of the silver on the trays will vary randomly following a normal distribution with a mean of 0.02 millimeter and a standard deviation o

> In Myers, Montgomery, and Anderson-Cook (2009), an application is discussed in which an engineer is concerned with the effects on the cracking of a titanium alloy. The three factors are A, temperature; B, titanium content; and C, amount of grain refiner.

> In a metallurgy experiment, it is desired to test the effect of four factors and their interactions on the concentration (percent by weight) of a particular phosphorus compound in casting material. The variables are A, percent phosphorus in the refinemen

> For Exercise 15.27, give all aliases for the six main effects. Exercise 15.27: There are six factors and only eight design points can be used. Construct a 26−3 by beginning with a 23 and use D = AB, E = −AC, and F = BC as the generators.

> Consider Exercise 15.27. Construct another 26−3 that is different from the design chosen in Exercise 15.27. Exercise 15.27: There are six factors and only eight design points can be used. Construct a 26−3 by beginning with a 23 and use D = AB, E = −AC,

> There are six factors and only eight design points can be used. Construct a 26−3 by beginning with a 23 and use D = AB, E = −AC, and F = BC as the generators.

> Consider a 25−1 design with factors A, B, C, D, and E. Construct the design by beginning with a 24 and use E = ABCD as the generator. Show all aliases.

> In the study Durability of Rubber to Steel Adhesively Bonded Joints, conducted at the Department of Environmental Science and Mechanics and analyzed by the Statistics Consulting Center at Virginia Tech, an experimenter measured the number of breakdowns i

> In an experiment conducted at the Department of Mechanical Engineering and analyzed by the Statistics Consulting Center at Virginia Tech, a sensor detects an electrical charge each time a turbine blade makes one rotation. The sensor then measures the amp

> An experiment is conducted so that an engineer can gain insight into the influence of sealing temperature A, cooling bar temperature B, percent polyethylene additive C, and pressure D on the seal strength (in grams per inch) of a bread-wrapper stock. A 1

> Seven factors are varied at two levels in an experiment involving only 16 trials. A 1/8 fraction of a 27 factorial experiment is used, with the defining contrasts being ACD, BEF, and CEG. The data are as follows: Perform an analysis of variance on all

> A random sample of 15 adults living in a small town were selected to estimate the proportion of voters favoring a certain candidate for mayor. Each individual was also asked if he or she was a college graduate. By letting Y and N designate the responses

> (a) Using the defining contrasts ABCE and ABDF, obtain a 1/4 fraction of a 26 design. (b) Show the analysis-of-variance table (sources of variation and degrees of freedom) for all appropriate tests, assuming that E and F do not interact and all three-fac

> Construct a 1/4 fraction of a 26 factorial design using ABCD and BDEF as the defining contrasts. Show what effects are aliased with the six main effects.

> In an experiment conducted by the Mining Engineering Department at Virginia Tech to study a particular filtering system for coal, a coagulant was added to a solution in a tank containing coal and sludge, which was then placed in a recirculation system in

> (a) Obtain a 1/2 fraction of a 24 factorial design using BCD as the defining contrast. (b) Divide the 1/2 fraction into 2 blocks of 4 units each by confounding ABC. (c) Show the analysis-of-variance table (sources of variation and degrees of freedom) for

> List the aliases for the various effects in a 25 factorial experiment when the defining contrast is ACDE.

> Consider Figure 15.14, which represents a 22 factorial with 3 center runs. If quadratic curvature is significant, what additional design points would you select that might allow the estimation of the terms x21, x22? Explain. Figure 15.14: -1, 1 1,

> Suppose a second replicate of the experiment in Exercise 15.13 could be performed. (a) Would a second replication of the blocking scheme of Exercise 15.13 be the best choice? (b) If the answer to part (a) is no, give the layout for a better choice for t

> Oil producers are interested in nickel alloys that are strong and corrosion resistant. An experiment was conducted in which yield strengths were compared for nickel alloy tensile specimens charged in solutions of sulfuric acid saturated with carbon disul

> An experiment is described in Myers, Montgomery, and Anderson-Cook (2009) in which optimum conditions are sought for storing bovine semen to obtain maximum survival. The variables are percent sodium citrate, percent glycerol, and equilibration time in ho

> Consider a 25 experiment where the experimental runs are on 4 different machines. Use the machines as blocks, and assume that all main effects and two-factor interactions may be important. (a) Which runs would be made on each of the 4 machines? (b) Which

> In Exercise 13.6 on page 519, use the Kruskal-Wallis test at the 0.05 level of significance to determine if the organic chemical solvents differ significantly in sorption rate. Exercise 13.6: A study measured the sorption (either absorption or adsorptio

> Consider Exercise 15.11. Suppose there was some experimental difficulty in making the runs. In fact, the total experiment had to be halted after only 4 runs. As a result, the abbreviated experiment is given by With only these runs, we have the signs fo

> In Myers, Montgomery, and Anderson-Cook (2009), a data set is discussed in which a 23 factorial is used by an engineer to study the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two level

> Consider Exercise 15.5. Compute all 15 effects and do normal probability plots of the effects. (a) Does it appear as if your assumption of negligible three- and four-factor interactions has merit? (b) Are the results of the effect plots consistent with w

> The following data are obtained from a 23 factorial experiment replicated three times. Evaluate the sums of squares for all factorial effects by the contrast method. Draw conclusions. Treatment Combination Rep 1 Rep 2 Rep 3 (1) 12 19 10 15 24 20 16

> An engineer is interested in the effects of cutting speed and tool geometry on the life in hours of a machine tool. Two cutting speeds and two different geometries are used. Three experimental tests are accomplished at each of the four combinations. The

> In Myers, Montgomery, and Anderson-Cook (2009), a scenario is discussed involving an auto bumper plating process. The response is the thickness of the material. Factors that may impact the thickness include amount of nickel (A) and pH (B). A two-factor e

> The extraction rate of a certain polymer is known to depend on the reaction temperature and the amount of catalyst used. An experiment was conducted at four levels of temperature and five levels of the catalyst, and the extraction rate was recorded in th

> An experiment was conducted to determine whether additives increase the adhesiveness of rubber products. Sixteen products were made with the new additive and another 16 without the new additive. The observed adhesiveness was as recorded below. Perform

> To determine which muscles need to be subjected to a conditioning program in order to improve one’s performance on the flat serve used in tennis, a study was conducted by the Department of Health, Physical Education and Recreation at Vi

> An experiment was designed for personnel in the Department of Animal Science at Virginia Tech to study urea and aqueous ammonia treatment of wheat straw. The purpose was to improve nutritional value for male sheep. The diet treatments were control, urea

> The following data represent the operating times in hours for three types of scientific pocket calculators before a recharge is required: Use the Kruskal-Wallis test, at the 0.01 level of significance, to test the hypothesis that the operating times fo

> Four laboratories are being used to perform chemical analysis. Samples of the same material are sent to the laboratories for analysis as part of a study to determine whether or not they give, on the average, the same results. The analytical results for t

> Consider the aggregate data of Example 13.1. Perform Bartlett’s test, at level α = 0.1, to determine if there is heterogeneity of variance among the aggregates.

> To ascertain the number of tellers needed during peak hours of operation, data were collected by an urban bank. Four tellers were studied during three “busy” times: (1) weekdays between 10:00 and 11:00 A.M., (2) weekda

> The manufacturer of a certain brand of freeze-dried coffee hopes to shorten the process time without jeopardizing the integrity of the product. The process engineer wants to use 3 temperatures for the drying chamber and 4 drying times. The current drying

> In the book SN-Ratio for the Quality Evaluation, published by the Japanese Standards Association (1988), a study on how tire air pressure affects the maneuverability of an automobile was described. Three different tire air pressures were compared on thre

> Corrosion fatigue in metals has been defined as the simultaneous action of cyclic stress and chemical attack on a metal structure. A widely used technique for minimizing corrosion fatigue damage in aluminum involves the application of a protective coatin

> Exercise 14.25 on page 588 describes an experiment involving the extraction of polyethylene through use of a solvent. (a) Do a different sort of analysis on the data. Fit an appropriate regression model with a solvent categorical variable, a temperatur

> A control valve needs to be very sensitive to the input voltage, thus generating a good output voltage. An engineer turns the control bolts to change the input voltage. The book SN-Ratio for the Quality Evaluation, published by the Japanese Standards Ass

> In the experiment of Review Exercise 14.33, cake volume was also used as a response. The units are cubic inches. Test for interaction between factors and discuss main effects. Assume that both factors are fixed effects. Exercise 14.33: The Statistics C

> The following data represent the weights, in kilograms, of personal luggage carried on various flights by a member of a baseball team and a member of a basketball team. Use the rank-sum test with α = 0.05 to test the null hypothesis that

> Let us assume that the prior distribution for the proportion p of drinks from a vending machine that overflow is p 0.05 0.10 0.15 π(p) 0.3 0.5 0.2 If 2 of the next 9 drinks from this machine overflow, find (a) the posterior distribution for the proportio

> Personnel in the Materials Engineering Department at Virginia Tech conducted an experiment to study the effects of environmental factors on the stability of a certain type of copper-nickel alloy. The basic response was the fatigue life of the material. T

> A study was made to determine if humidity conditions have an effect on the force required to pull apart pieces of glued plastic. Three types of plastic were tested using 4 different levels of humidity. The results, in kilograms, are as follows: (a) Ass

> An experiment was conducted in the Department of Food Science at Virginia Tech. It was of interest to characterize the texture of certain types of fish in the herring family. The effect of sauce types used in preparing the fish was also studied. The resp

> The Statistics Consulting Center at Virginia Tech was involved in analyzing a set of data taken by personnel in the Human Nutrition and Foods Department in which it was of interest to study the effects of flour type and percent sweetener on certain physi

> A process engineer wants to determine if the power setting on the machines used to fill certain types of cereal boxes results in a significant effect on the actual weight of the product. The study consists of 3 randomly chosen types of cereal manufacture

> A manufacturer of latex house paint (brand A) would like to show that its paint is more robust to the material being painted than that of its two closest competitors. The response is the time, in years, until chipping occurs. The study involves the three

> A plant manager would like to show that the yield of a woven fabric in the plant does not depend on machine operator or time of day and is consistently high. Four randomly selected operators and 3 randomly selected hours of the day are chosen for the stu

> Three strains of rats were studied under 2 environmental conditions for their performance in a maze test. The error scores for the 48 rats were recorded. Use a 0.01 level of significance to test the hypothesis that (a) there is no difference in error s

> Consider the following analysis of variance for a random effects experiment: Test for significant variance components among all main effects and interaction effects at the 0.01 level of significance (a) by using a pooled estimate of error when appropri

> A defense contractor is interested in studying an inspection process to detect failure or fatigue of transformer parts. Three levels of inspections are used by three randomly chosen inspectors. Five lots are used for each combination in the study. The fa

> From a mathematics class of 12 equally capable students using programmed materials, 5 students are selected at random and given additional instruction by the teacher. The results on the final examination are as follows: Use the rank-sum test with &Icir

> To estimate the various components of variability in a filtration process, the percent of material lost in the mother liquor is measured for 12 experimental conditions, with 3 runs on each condition. Three filters and 4 operators are selected at random f

> Assuming a random effects experiment for Exercise 14.2 on page 575, estimate the variance components for brand of orange juice concentrate, for number of days from when orange juice was blended until it was tested, and for experimental error. Exercise 1

> In the book Design of Experiments for Quality Improvement, published by the Japanese Standards Association (1989), a study is reported on the extraction of polyethylene by using a solvent and how the amount of gel (proportion) is influenced by three fact

> A scientist collects experimental data on the radius of a propellant grain, y, as a function of powder temperature, extrusion rate, and die temperature. Resources are not available to make repeated experimental trials at the eight combinations of facto

> Consider combinations of three factors in the removal of dirt from standard loads of laundry. The first factor is the brand of the detergent, X, Y , or Z. The second factor is the type of detergent, liquid or powder. The third factor is the temperature o

> Consider the data set in Exercise 14.21. (a) Construct an interaction plot for any two-factor interaction that is significant. (b) Do a normal probability plot of residuals and comment. Exercise 14.21: Electronic copiers make copies by gluing black ink

> Electronic copiers make copies by gluing black ink on paper, using static electricity. Heating and gluing the ink on the paper comprise the final stage of the copying process. The gluing power during this final process determines the quality of the copy.

> For a study of the hardness of gold dental fillings, five randomly chosen dentists were assigned combinations of three methods of condensation and two types of gold. The hardness was measured. (See Hoaglin, Mosteller, and Tukey, 1991.) Let the dentists p

> To ascertain the stability of vitamin C in reconstituted frozen orange juice concentrate stored in a refrigerator for a period of up to one week, the study Vitamin C Retention in Reconstituted Frozen Orange Juice was conducted by the Department of Human

> Corrosion fatigue in metals has been defined as the simultaneous action of cyclic stress and chemical attack on a metal structure. In the study Effect of Humidity and Several Surface Coatings on the Fatigue Life of 2024-T351 Aluminum Alloy, conducted by

> A fishing line is being manufactured by two processes. To determine if there is a difference in the mean breaking strength of the lines, 10 pieces manufactured by each process are selected and then tested for breaking strength. The results are as follows

> The method of X-ray fluorescence is an important analytical tool for determining the concentration of material in solid missile propellants. In the paper An X-ray Fluorescence Method for Analyzing Polybutadiene Acrylic Acid (PBAA) Propellants (Quarterly

> The following data are measurements from an experiment conducted using three factors A, B, and C, all fixed effects: (a) Perform tests of significance on all interactions at the α = 0.05 level. (b) Perform tests of significance on the mai

> Consider an experimental situation involving factors A, B, and C, where we assume a three-way fixed effects model of the form yijkl = μ + αi + βj + γk+(βγ)jk+ €i

> The purpose of the study The Incorporation of a Chelating Agent into a Flame Retardant Finish of a Cotton Flannelette and the Evaluation of Selected Fabric Properties, conducted at Virginia Tech, was to evaluate the use of a chelating agent as part of th

> Consider the data set in Exercise 14.12 and answer the following questions. (a) Both factors, copper and time, are quantitative in nature. As a result, a regression model may be of interest. Describe what might be an appropriate model using x1 = copper c

> In Myers, Classical and Modern Regression with Applications (Duxbury Classic Series, 2nd edition, 1990), an experiment is described in which the Environmental Protection Agency seeks to determine the effect of two water treatment methods on magnesium upt

> In an experiment conducted in the Civil Engineering Department at Virginia Tech, growth of a certain type of algae in water was observed as a function of time and the dosage of copper added to the water. The data are as follows. Response is in units of a

> A study was done to determine the impact of two factors, method of analysis and the laboratory doing the analysis, on the level of sulfur content in coal. Twenty-eight coal specimens were randomly assigned to 14 factor combinations, the structure of the

> Two factors in a manufacturing process for an integrated circuit are studied in a two-factor experiment. The purpose of the experiment is to learn their effect on the resistivity of the wafer. The factors are implant dose (2 levels) and furnace position

> An experiment was conducted to study the effects of temperature and type of oven on the life of a particular component. Four types of ovens and 3 temperature levels were used in the experiment. Twenty-four pieces were assigned randomly, two to each combi

> The following data represent the number of hours that two different types of scientific pocket calculators operate before a recharge is required. Use the rank-sum test with α = 0.01 to determine if calculator A operates longer than calcul

> Use Bartlett’s test at the 0.01 level of significance to test for homogeneity of variances in Exercise 13.5 on page 519. Exercise 13.5:

> For the data set in Exercise 13.7, use Bartlett’s test to check whether the variances are equal. Use α = 0.05. Exercise 13.7: It has been shown that the fertilizer magnesium ammonium phosphate, MgNH4PO4, is an effective s

> It has been shown that the fertilizer magnesium ammonium phosphate, MgNH4PO4, is an effective supplier of the nutrients necessary for plant growth. The compounds supplied by this fertilizer are highly soluble in water, allowing the fertilizer to be appli

> A study measured the sorption (either absorption or adsorption) rates of three different types of organic chemical solvents. These solvents are used to clean industrial fabricated-metal parts and are potential hazardous waste. Independent samples from ea

> The mitochondrial enzyme NADPH: NAD transhydrogenase of the common rat tapeworm (Hymenolepiasis diminuta) catalyzes hydrogen in the transfer from NADPH to NAD, producing NADH. This enzyme is known to serve a vital role in the tapeworm’s

> An analysis was conducted by the Statistics Consulting Center at Virginia Tech in conjunction with the Department of Forestry. A certain treatment was applied to a set of tree stumps in which the chemical Garlon was used with the purpose of regenerating

> A textile company weaves a certain fabric on a large number of looms. The managers would like the looms to be homogeneous so that their fabric is of uniform strength. It is suspected that there may be significant variation in strength among looms. Consid

> Five “pours” of metals have had 5 core samples each analyzed for the amount of a trace element. The data for the 5 randomly selected pours are as follows: (a) The intent is that the pours be identical. Thus, test th

2.99

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