Question: Three varieties of potatoes are being compared

> 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

> Immobilization of free-ranging white-tailed deer by drugs allows researchers the opportunity to closely examine the deer and gather valuable physiological information. In the study Influence of Physical Restraint and Restraint Facilitating Drugs on Blood

> The following data show the effect of 4 operators, chosen randomly, on the output of a particular machine. (a) Perform a random effects analysis of variance at the 0.05 level of significance. (b) Compute an estimate of the operator variance component

> To find out whether a new serum will arrest leukemia, nine patients, who have all reached an advanced stage of the disease, are selected. Five patients receive the treatment and four do not. The survival times, in years, from the time the experiment comm

> An experiment is conducted in which 4 treatments are to be compared in 5 blocks. The data are given below. (a) Assuming a random effects model, test the hypothesis, at the 0.05 level of significance, that there is no difference between treatment means

> Testing patient blood samples for HIV antibodies, a spectrophotometer determines the optical density of each sample. Optical density is measured as the absorbance of light at a particular wavelength. The blood sample is positive if it exceeds a certain c

> An experiment was conducted to compare three types of coating materials for copper wire. The purpose of the coating is to eliminate “flaws” in the wire. Ten different specimens of length 5 millimeters were randomly ass

> In the book Design of Experiments for the Quality Improvement, published by the Japanese Standards Association (1989), a study on the amount of dye needed to get the best color for a certain type of fabric was reported. The three amounts of dye, 1 3% wof

> In the paper “Self-Control and Therapist Control in the Behavioral Treatment of Overweight Women,” published in Behavioral Research and Therapy (Vol. 10, 1972), two reduction treatments and a control treatment were stu

> Scientists in the Department of Plant Pathology at Virginia Tech devised an experiment in which 5 different treatments were applied to 6 different locations in an apple orchard to determine if there were significant differences in growth among the treatm

> Organic arsenicals are used by forestry personnel as silvicides. The amount of arsenic that the body takes in when exposed to these silvicides is a major health problem. It is important that the amount of exposure be determined quickly so that a field wo

> In a study conducted by the Department of Health and Physical Education at Virginia Tech, 3 diets were assigned for a period of 3 days to each of 6 subjects in a randomized complete block design. The subjects, playing the role of blocks, were assigned th

> A nuclear power facility produces a vast amount of heat, which is usually discharged into aquatic systems. This heat raises the temperature of the aquatic system, resulting in a greater concentration of chlorophyll a, which in turn extends the growing se

> In an article “Shelf-Space Strategy in Retailing,” published in Proceedings: Southern Marketing Association, the effect of shelf height on the supermarket sales of canned dog food is investigated. An experiment was con

> A random sample X1, . . . , Xn comes from a uniform distribution (see Section 6.1) population U(0, θ) with unknown θ. The data are given below: 0.13, 1.06, 1.65, 1.73, 0.95, 0.56, 2.14, 0.33, 1.22, 0.20, 1.55, 1.18, 0.71, 0.01,

> In a study on The Periphyton of the South River, Virginia: Mercury Concentration, Productivity, and Autotropic Index Studies, conducted by the Department of Environmental Sciences and Engineering at Virginia Tech, the total mercury concentration in perip

> The following data represent the final grades obtained by 5 students in mathematics, English, French, and biology: Test the hypothesis that the courses are of equal difficulty. Use a P-value in your conclusions and discuss your findings. Subject S

> The following data are the percents of foreign additives measured by 5 analysts for 3 similar brands of strawberry jam, A, B, and C: Perform a randomized complete block analysis of variance to test the hypothesis, at the 0.05 level of significance, th

> Four kinds of fertilizer f1, f2, f3, and f4 are used to study the yield of beans. The soil is divided into 3 blocks, each containing 4 homogeneous plots. The yields in kilograms per plot and the corresponding treatments are as follows: Conduct an anal

> The financial structure of a firm refers to the way the firm’s assets are divided into equity and debt, and the financial leverage refers to the percentage of assets financed by debt. In the paper The Effect of Financial Leverage on Ret

> In a biological experiment, four concentrations of a certain chemical are used to enhance the growth of a certain type of plant over time. Five plants are used at each concentration, and the growth in each plant is measured in centimeters. The following

> Do Duncan’s test for paired comparisons for the data of Exercise 13.6 on page 519. Discuss the results. Exercise 13.6: A study measured the sorption (either absorption or adsorption) rates of three different types of organic chemical s

> The printout in Figure 13.5 on page 532 gives information on Duncan’s test, using PROC GLM in SAS, for the aggregate data in Example 13.1. Give conclusions regarding paired comparisons using Duncan’s test results. Fig

> The following table (from A. Hald, Statistical Theory with Engineering Applications, John Wiley & Sons, New York, 1952) gives tensile strengths (in deviations from 340) for wires taken from nine cables to be used for a high-voltage network. Each cabl

> A random variable X follows an exponential distribution with mean 1/β. Assume the prior distribution of β is another exponential distribution with mean 2.5. Determine the Bayes estimate of β under the absolute-error loss function.

> The data in the following table represent the number of hours of relief provided by five different brands of headache tablets administered to 25 subjects experiencing fevers of 38â—¦C or more. Perform the analysis of variance and test t

> It is suspected that the environmental temperature at which batteries are activated affects their life. Thirty homogeneous batteries were tested, six at each of five temperatures, and the data are shown below (activated life in seconds). Analyze and inte

> The following data are values of pressure (psi) in a torsion spring for several settings of the angle between the legs of the spring in a free position: Compute a one-way analysis of variance for this experiment and state your conclusion concerning th

> In the study An Evaluation of the Removal Method for Estimating Benthic Populations and Diversity conducted by Virginia Tech on the Jackson River, 5 different sampling procedures were used to determine the species counts. Twenty samples were selected at

> An investigation was conducted to determine the source of reduction in yield of a certain chemical product. It was known that the loss in yield occurred in the mother liquor, that is, the material removed at the filtration stage. It was thought that diff

> Use Tukey’s test, with a 0.05 level of significance, to analyze the means of the five different brands of headache tablets in Exercise 13.2 on page 518. Exercise 13.2:

> The study Loss of Nitrogen Through Sweat by Preadolescent Boys Consuming Three Levels of Dietary Protein was conducted by the Department of Human Nutrition and Foods at Virginia Tech to determine perspiration nitrogen loss at various dietary protein leve

> 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 the

> Consider the data of Review Exercise 13.45 on page 555. Make significance tests on the following contrasts: (a) B versus A, C, and D; (b) C versus A and D; (c) A versus D. Exercise 13.45: Four laboratories are being used to perform chemical analysis. Sa

> Use Bartlett’s test at the 0.05 level of significance to test for homogeneity of variances in Exercise 13.6 on page 519. Exercise 13.6: A study measured the sorption (either absorption or adsorption) rates of three different types of o

> A random variable X follows a negative binomial distribution with parameters k = 5 and p [i.e.,b ∗ (x; 5, p)]. Furthermore, we know that p follows a uniform distribution on the interval (0, 1). Find the Bayes estimate of p under the squared-error loss fu

> Use Cochran’s test at the 0.01 level of significance to test for homogeneity of variances in Exercise 13.4 on page 519. Exercise 13.4: Immobilization of free-ranging white-tailed deer by drugs allows researchers the opportunity to clos

> Six different machines are being considered for use in manufacturing rubber seals. The machines are being compared with respect to tensile strength of the product. A random sample of four seals from each machine is used to determine whether the mean tens

> (a) Fit a multiple regression equation of the form μY |x = β0 + β1x + β2x2 to the data of Example 11.8 on page 420. (b) Estimate the yield of the chemical reaction for a temperature of 225 ◦ C.

> The following is a set of coded experimental data on the compressive strength of a particular alloy at various values of the concentration of some additive: (a) Estimate the quadratic regression equation μY |x = β0 + Î&s

> An experiment was conducted in order to determine if cerebral blood flow in human beings can be predicted from arterial oxygen tension (millimeters of mercury). Fifteen patients participated in the study, and the following data were collected: Estimat

> An experiment was conducted on a new model of a particular make of automobile to determine the stopping distance at various speeds. The following data were recorded. (a) Fit a multiple regression curve of the form μD|v = β0 +

> Rayon whiteness is an important factor for scientists dealing in fabric quality. Whiteness is affected by pulp quality and other processing variables. Some of the variables include acid bath temperature, â—¦ C (x1); cascade acid concent

> A client from the Department of Mechanical Engineering approached the Consulting Center at Virginia Tech for help in analyzing an experiment dealing with gas turbine engines. The voltage output of engines was measured at various combinations of blade spe

> For the quadratic model of Exercise 12.51(b), give estimates of the variances and covariances of the estimates of β1 and β11. Exercise 12.51(b): The following is a set of data for y, the amount of money (in thousands of dollars)

> For the model of Exercise 12.50(a), test the hypothesis H0: β4 = 0, H1: β4 ≠ 0. Use a P-value in your conclusion. Exercise 12.50(a): For the punter data in Case Study 12.2, an additional response, â€

> Suppose that a sample consisting of 5, 6, 6, 7, 5, 6, 4, 9, 3, and 6 comes from a Poisson population with mean λ. Assume that the parameter λ follows a gamma distribution with parameters (3, 2). Under the squared-error loss function, find the Bayes estim

> The following is a set of data for y, the amount of money (in thousands of dollars) contributed to the alumni association at Virginia Tech by the Class of 1960, and x, the number of years following graduation: (a) Fit a regression model of the type &Ici

> For the punter data in Case Study 12.2, an additional response, “punting distance,” was also recorded. The average distance values for each of the 13 punters are given. (a) Using the distance data rather than the hang

> The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature x1, the number of days in the month x2, the average product purity x3, and the tons of product produced x4. The past yearâ€&

> Use the techniques of backward elimination with α = 0.05 to choose a prediction equation for the data of Table 12.8.

> For the data of Exercise 12.15 on page 452, use the techniques of (a) forward selection with a 0.05 level of significance to choose a linear regression model; (b) backward elimination with a 0.05 level of significance to choose a linear regression mode

> Consider the “hang time” punting data given in Case Study 12.2, using only the variables x2 and x3. (a) Verify the regression equation shown on page 489. (b) Predict punter hang time for a punter with LLS = 180 pounds and Power = 260 foot-pounds. (c) C

> A study was done to determine whether the gender of the credit card holder was an important factor in generating profit for a certain credit card company. The variables considered were income, the number of family members, and the gender of the card hold

> A study was done to assess the cost effectiveness of driving a four-door sedan instead of a van or an SUV (sports utility vehicle). The continuous variables are odometer reading and octane of the gasoline used. The response variable is miles per gallon.

> For the data set given in Exericise 12.16 on page 453, can the response be explained adequately by any two regressor variables? Discuss. Exericise 12.16: An engineer at a semiconductor company wants to model the relationship between the gain or hFE of a

> Consider the data of Exercise 12.13 on page 452. Can the response, wear, be explained adequately by a single variable (either viscosity or load) in an SLR rather than with the full two-variable regression? Justify your answer thoroughly through tests of

> Suppose that the time to failure T of a certain hinge is an exponential random variable with probability density f(t) = θe−θt, t>0. From prior experience we are led to believe that θ is a value

> In Example 12.8, a case is made for eliminating x1, powder temperature, from the model since the P-value based on the F-test is 0.2156 while P-values for x2 and x3 are near zero. (a) Reduce the model by eliminating x1, thereby producing a full and a rest

> Consider Example 12.3 on page 447. Compare the two competing models. First order: yi = β0 + β1x1i + β2x2i + €i, Second order: yi = β0 + β1x1i + β2x2i+ β11x21i + β22x22i + β12x1ix2i + i. Use R2adj in your comparison. Test H0 : β11 = β22 =β12 = 0. In addit

> Consider Example 12.4. Figure 12.1 on page 459 displays a SAS printout of an analysis of the model containing variables x1, x2, and x3. Focus on the confidence interval of the mean response μY at the (x1, x2, x3) locations representing the 13 data points

> An experiment was conducted to determine if the weight of an animal can be predicted after a given period of time on the basis of the initial weight of the animal and the amount of feed that was eaten. The following data, measured in kilograms, were reco

> Consider the data of Exercise 11.55 on page 437. Fit a regression model using weight and drive ratio as explanatory variables. Compare this model with the SLR (simple linear regression) model using weight alone. Use R2, R2adj, and any t-statistics (or F-

> Consider the data for Exercise 12.36. Compute the following: R(β1 | β0), R(β1 | β0, β2, β3), R(β2 | β0, β1), R(β2 | β0, &I

> Consider the electric power data of Exercise 12.5 on page 450. Test H0: β1 = β2 = 0, making use of R(β1, β2 | β3, β4). Give a P-value, and draw conclusions. Exercise 12.5: The elec

> A small experiment was conducted to fit a multiple regression equation relating the yield y to temperature x1, reaction time x2, and concentration of one of the reactants x3. Two levels of each variable were chosen, and measurements corresponding to the

> Repeat Exercise 12.17 on page 461 using an F-statistic. Exercise 12.17: For the data of Exercise 12.2 on page 450, estimate σ2. Exercise 12.2: In Applied Spectroscopy, the infrared reflectance spectra properties of a viscous liquid used in

> For the model of Exercise 12.5 on page 450, test the hypothesis H0: β1 = β2 = 0, H1: β1 and β2 are not both zero. Exercise 12.5: The electric power consumed each month by a chemical plant is thought to be

> Suppose that in Example 18.7 the electrical firm does not have enough prior information regarding the population mean length of life to be able to assume a normal distribution for μ. The firm believes, however, that μ is surel