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organization theory and design

Questions and Answers of Organization Theory and Design

8. Weld strength experiment, continued For the experiment described in Exercise 7, use the two-way complete model instead of the equivalent cell means model. (a) Test the hypothesis of no
7. Weld strength experiment The data shown in Table 6.22 are a subset of the data given by Anderson and McLean (1974) and show the strength of a weld in a steel bar. Two factors of interest were gage
6. Battery experiment, continued Consider the battery experiment introduced in Sect. 2.5.2, p. 24, for which a = b = 2 and r = 4. Suppose it is of interest to calculate confidence intervals for the
5. Weight Lifting Experiment (Gary Mirka 1986) The experimenter was interested in the effect on pulse rate (heart rate) of lifting different weights with legs either straight or bent (factor A, coded
4. Show that when the parentheses is expanded in formula (6.4.15) forssE on p. 151, the computational formula (6.4.16) is obtained.
3. Consider the functions {α∗ 1 − α∗ 2} and {(αβ)11 − (αβ)21 − (αβ)12 + (αβ)22} under the two-way complete model (6.2.2). (a) Verify that the functions are estimable contrasts.
2. Verify that (τij − τ i. − τ .j + τ ..) is an interaction contrast for the two-way complete model. Write down the list of contrast coefficients in terms of the τij’s when factor A has a
1. Under what circumstances should the two-way main effects model (6.2.3) be used rather than the two-way complete model (6.2.2)? Discuss the interpretation of main effects in each model.
9. Spaghetti sauce experiment (K. Brewster, E. Cesmeli, J, Kosa, M. Smith, and M. Soliman 1996) The spaghetti sauce experiment was run to compare the thicknesses of three particular brands of
8. Wildflower experiment (Barbra Foderaro 1986) An experiment was run to determine whether or not the germination rate of the endangered species of Ohio plant Froelichia floridana is affected by
7. Dessert experiment (P. Clingan, Y. Deng, M. Geil, J. Mesaros, and J. Whitmore, 1996) The experimenters were interested in whether the melting rate of a frozen orange dessert would be affected
6. Bicycle experiment (Debra Schomer 1987) The bicycle experiment was run to compare the crank rates required to keep a bicycle at certain speeds, when the bicycle was in twelfth gear on flat ground.
5. Catalyst experiment H. Smith, in the 1969 volume of Journal of Quality Technology, described an experiment that investigated the effect of four reagents and three catalysts on the production rate
4. Reaction time experiment, continued The reaction time pilot experiment was described in Exercise 4 of Chap. 4. The experimenters were interested in the different effects on the reaction time of
3. Margarine experiment (Amy L. Phelps, 1987) The data in Table 5.16 are the melting times in seconds for three different brands of margarine (coded 1–3) and one brand of butter (coded 4). The
2. Soap experiment, continued Check the assumptions on the one-way analysis of variance model (3.3.1) for the soap experiment, which was introduced in Sect. 2.5.1. The data are reproduced in Table
1. Meat cooking experiment, continued Check the assumptions on the one-way analysis of variance model (3.3.1) for the meat cooking experiment, which was introduced in Exercise 14 of Chap. 3. The data
10. Trout experiment, continued Consider again the trout experiment in Exercise 15 of Chap. 3. (a) Suppose the experiment were to be repeated. Suggest the largest likely value for the error mean
9. Battery experiment, continued Suppose the battery experiment of Sect. 2.5.2 (p. 24) is to be repeated. The experiment involved four treatments, and the error standard deviation is estimated from
8. Trout experiment, continued (a) For the trout experiment in Exercise 15 of Chap. 3 (see p. 67), test the hypotheses that the linear and quadratic trends in hemoglobin content of trout blood due to
7. Soap experiment, continued The soap experiment was described in Sect. 2.5.1, p. 20, and an analysis was given in Sect. 3.7.2, p. 50. (a) Suppose that the experimenter had been interested only in
6. Battery experiment, continued In Example 4.4.3 (page 89), Tukey’s method is used to obtain a set of 95% simultaneous confidence intervals for the pairwise differences τi − τs. Verify that
5. Trout experiment, continued Exercise 15 of Chap. 3 (p. 67) concerns a study of the effects of four levels of sulfamerazine (0, 5, 10, 15 g per 100 lb of fish) on the hemoglobin content of trout
4. Reaction time experiment (L. Cai, T. Li, Nishant, and A. van der Kouwe, 1996) The experiment was run to compare the effects of auditory and visual cues on speed of response of a human subject. A
3. Meat cooking experiment, continued The meat cooking experiment was described in Exercise 14 of Chap. 3, and the data were given in Table 3.14, p. 68. (a) Compare the effects of the six treatments,
2. Cotton-spinning experiment, continued For the cotton-spinning experiment of Sect. 2.3, p. 13, identify any contrasts or functions that you think might be interesting to estimate. For any contrasts
1. Buoyancy experiment Consider conducting an experiment to investigate the question, “Is the buoyancy of an object in water affected by different concentrations of salt in the water?” (a)
19. An experiment is to be run to determine whether or not time differences in performing a simple manual task are caused by different types of lighting. Five levels of lighting are selected ranging
18. The diameter of a ball bearing is to be measured using three different calipers. How many observa- tions should be taken on each caliper type if the null hypothesis Ho: (effects of the calipers
17. Meat cooking experiment, continued Suppose the meat cooking experiment of Exercise 3.14 is to be repeated with the same v = 6 treatments, and suppose the same hypothesis, that the treatments have
16. Trout experiment, continued Suppose the trout experiment of Exercise 3.15 is to be repeated with the same v = 4 treatments, and suppose that the same hypothesis, that the treatments have no
15. Trout experiment (Gutsell 1951, Biometrics) The data in Table 3.15 show the measurements of hemoglobin (grams per 100 ml) in the blood of brown trout. The trout were placed at random in four
14. Meat cooking experiment (L. Alvarez, M. Burke, R. Chow, S. Lopez, and C. Shirk, 1998)An experiment was run to investigate the amount of weight lost (in grams) by ground beef hamburgers after
13. Heart–lung pump experiment, continued The heart–lung pump experiment was described in Example 3.4.1, p. 37, and the data were shown in Table 3.2, p. 38. (a) Calculate an analysis of variance
12. Balloon experiment Prior to 1985, the experimenter (Meily Lin) had observed that some colors of birthday balloons seem to be harder to inflate than others. She ran this experiment to determine
11. Verify, for the one-way analysis of variance model (3.3.1), p. 33, that each treatment sample variance S2 i is an unbiased estimator of the error varianceσ2, so that
10. For the model in the previous exercise, find an unbiased estimator for σ2. Compare the estimator with that in (3.4.7), p. 39.
9. (requires calculus) Find the least squares estimates ofμ1, μ2, …, μv for the linear modelYit = μi + it (t = 1,...,ri ; i = 1, 2,...,v), where the it’s are independent random variables
8. For the model in the previous exercise, find an unbiased estimator forσ2. (Hint: first calculate E[ssE0]in (3.5.10), p. 42.)
7. (requires calculus) Show that the least squares estimator ofμ + τ is Y .. for the linear modelYit = μ+τ +0 it (t = 1,...,ri ; i = 1, 2,...,v), where the 0 it’s are independent random
6. (requires calculus) Show that the normal equations for estimating μ, τ1,..., τv are those given in Eq. (3.4.3) on p. 35.
5. Consider a completely randomized design with observations on three treatments (coded 1, 2, 3). For the one-way analysis of variance model (3.3.1), p. 33, determine which of the following are
4. For the one-way analysis of variance model (3.3.1), p. 33, the solution to the normal equations used by the SAS software is τˆi = yi. − yv. (i = 1,...,v) andμˆ = yv.. (a) Is τi estimable?
2. Suppose that you are planning to run an experiment with one treatment factor having three levels and no blocking factors. It has been determined that r1 = 3, r2 = r3 = 5. Assign at random 13
1. Suppose that you are planning to run an experiment with one treatment factor having four levels and no blocking factors. Suppose that the calculation of the required number of observations has
9. The following description was given by Clifford Pugh in the 1953 volume of Applied Statistics.
8. Read critically through the checklists in Sect. 2.5. Would you suggest any changes? Would you have done anything differently? If you had to criticize these experiments, which points would you
7. For experiment 8, write down all the possible sources of variation. In your opinion, should this experiment be run as a completely randomized design, a block design, or a design with more than one
6. For experiment 6, specify what measurements should be made, how they should be made, and list any difficulties that might be expected.
13.7 Suppose a researcher comes to you to get some help on the analysis of the fol- lowing data set:where each represents an observation. (i) What questions would you ask the investigator before you
For an experiment with four input variables, construct a Box-Behnken design using the following BIBD with four treatments and six blocks of size 2: Treatment 1 123 y 4 Blocks 2 3 4 5 6 X X x X X X X
11.6 A horticultural experiment conducted in a green house was laid out as a Latin square design, where the blocking factors represent temperature and light inten- sity, respectively. The treatments
A Grco-Latin square in its pure form may not be very useful, but extension and replications of it often prove to be quite useful. Consider the following design:where rows, columns and Greek letters
Suppose a poultry scientist comes to you to help him set up an experiment. He wants to compare the effects of 3 different diets (treatments) on eggshell prop- erties. He has available 6 strains of
9.11 Consider a RCBD with subsampling. Specifically, suppose 3 treatments, b = 4 blocks, and n = 2 observations per experimental unit. (i) Give a linear model for data from such an experiment. (ii)
9.9 Consider the following experimental data:(i) Do the exact analysis, obtaining the ANOVA table, LS means for treat- ments, and the estimated variance for simple treatment comparisons (use SAS PROC
9.8 Suppose a researcher comes to you for advice about the analysis of an experiment she has conducted. She has used 5 treatments and she has 9 observations for each treatment. She shows you the
9.7 A researcher comes to you with data from a block design. For comparing 4 treat- ments he has used 5 blocks each with 4 experimental units. He took 2 measure- ments on each experimental unit. He
9.5 Suppose a researcher comes to you with a table of data, obtained from a block design, that looks as follows:where each x represents one observation. She asks you to analyze the data. (i) How
9.4 In a study of reaction time under the influence of alcohol, age is thought to be another factor that could affect the time. Test subjects (individuals) were classified into three age groups:
9.3 A chemist wants to compare three treatments. The experimental material he plans to use comes from four different manufacturers. He expects systematic differences among the material from the
9.2 Consider an experiment with 5 treatments in a RCB design with 10 blocks. The partial ANOVA table is as follows:(i) Complete the ANOVA table above. (ii) Give the test statistic for testing Ho T =
9.1 Consider the following data from an experiment testing the effects of 5 levels of application of potash on the Pressley strength index of cotton (John and Que- nouille, 1977)(i) Obtain the ANOVA
Show that[see (8. 39)]. av. var () 1 TIZ t-1 Exa
Suppose an engineer is interested in comparing three chemical processes for manufacturing a certain compound. She suspects that the impurity of the raw material used in the processes will affect the
An experiment was conducted to compare six different management techniques (such as pruning, spraying and fertilizing) for apple trees with respect to yield. Each apple tree represents an
Consider the following data (y, x) from a CRD, where y represents the response after treatment, and is a covariate.(i) Analyze the data, ignoring the covariate, that is, (a) obtain treatment means,
7.2 Consider a CRD with 5 treatments, 6 replications for each treatment and 4 obser- vations for every experimental unit. Suppose the treatments represent increasing amounts (x) of fertilizer applied
7.1 Consider an experiment to investigate the effects of sugar on the length of pea sections grown in tissue culture. A CRD is used with 5 replications for each of the treatments: T: Control (nothing
6.5 For the CRD with t treatments, r' replications per treatment and n observations per EU, show that var cii.. Ciyi.. = + no p'n
6.4 A pharmaceutical company conducts an experiment to compare 5 drugs. 30 animals are available for the trial. Each drug is injected into 6 randomly selected animals. All the animals are very
6.3 An agronomist conducted a field trial to compare the relative effects of five par- ticular fertilizers on the yield of Trebi barley. Thirty homogeneous experimental plots are available and six
6.2 A researcher has done a preliminary study in the form of a CRD with subsam- pling to help him decide on the final design. He wants to compare five (5) treat- ments. In the preliminary study he
6.1 Consider the following results from a CRD with t = 2 treatments and r = 4 replications for each treatment:(i) Using the ratio MS(T)/MS (E) as the test criterion perform the randomiza- tion test
A complete set of linearly independent functions for the linear model y = X3+ e is a set of rx linearly independent functions X3(k = 1, 2,....rx), where rx is the rank of X, such that all estimable
(i) Give a definition for connectedness in a three-way cross-classification as- suming that all interactions are zero.(ii) Consider the three-way classification with factors A, B, C, where each
For the three-way cross-classification write out all possible well-defined models.
Consider the following balanced data structure: We have four factors A, B, C, D, where A and B are crossed, C is nested in AB and D is nested in C. (1) Draw a structure diagram. (ii) Give all
Prove that (4.22), with appropriate conditions on C. is a solution of (4.20).
Prove that X'X rank %) = -rank (c)+rank(C).
Refer to Section 4.6.2 and prove that X'DX is s.i.p. and equals X[X(I- C+C)]+.
Prove the basic properties (i). (ii), (iii) and (iv) of the NE (4.20).
Prove that the NE for y = X3 C3=C is given by (4.20).
Verify that A+ of Example 4.2 satisfies the properties of a Moore-Penrose in- verse.
Verify that A of Example 4.1 satisfies the properties of a generalized inverse.
Prove that the shortest solution of a consistent set of equations Ax = b is x = A+b.
Prove that there exists a p such that X'Xp = A implies X' = a'X and vice versa.
Prove that the NE X'Xb = X'y is consistent in b for all y.
Reconsider the data from the injection molding experiment in Table 12.13.(a) Fit the model y = 0 + AXA + BXB + A×BXAXB in the adjustment factors using the method of least squares.(b) Simultaneously
Consider the data for the product array design for the elastometric connec-tor shown in Figure 12.4.(a) Calculate the mean pull-o force and log variance of the pull-o force across the noise array for
In the design of a thin lm redistribution layer (cited by J. Lorenzen, IBM Kingston and discussed by Lawson and Madrigal (1994)), the cir-cuit impedance (Z) is a function of three design factors: the
An experiment originally performed by the National Railway Corpora-tion of Japan (Taguchi and Wu, 1980) was reanalyzed by Box and Meyer(1986b). The control factors in the design were A, kind of
Taguchi (1987) described an experiment to nd the source of clutch slip-ping in automobiles. Prototype clutches were assembled using some new components and some components taken from disassembled
Because the elastometric connector experiments described in Section 12.3 required physical experimentation, Song and Lawson (1988) suggested us-ing a single array design to save on the number of
The noise factors were E, purity of the recycled solvent; and D, purity of reagent 1 that comes from a supplier. A product-array design was used for the experiment that is shown in Table 12.20. The
Lawson (1990) describes an experiment in a chemical process with the aim of producing less byproduct tars. The control factors were A, reaction temperature; B, catalyst concentration; and C, excess
Reconsider the cake mix experiment described in exercise 9 of Chapter 8.The control factors that can be selected by the manufacturer are F: the amount of our; S: the amount of shortening; and E: the
Consider the commercial product test of erasers conducted by Sachiyo and Kosaka in 1971 and discussed by Taguchi (1987). The purpose of the test was to determine the quality of erasure when lines of
Cornell (1988) presented the original example of mixture experiment for producing vinyl for automobile seat covers. The data is shown in Table 11.14, and the variable names are the same as those
Steiner et al. (2007) describe a mixture-process variable (MPV) experiment conducted by students to nd an optimal homemade bubble solution for use in a battery operated bubble-blowing toy. The

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