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Probability And Statistics For Engineering And The Sciences 9th Edition Jay L. Devore - Solutions

Numerous factors contribute to the smooth running of an electric motor ("Increasing Market Share Through Improved Product and Process Design: An Experimental Approach," Quality Engineering, 1991: 361-369). In particular, it is desirable to keep motor noise and vibration to a minimum. To study the
An article in the British scientific journal Nature ("Sucrose Induction of Hepatic Hyperplasia in the Rat," August 25, 1972: 461) reports on an experiment in which each of five groups consisting of six rats was put on a diet with a different carbohydrate. At the conclusion of the experiment, the
Referring to Exercise 38, An article in the British scientific journal Nature ("Sucrose Induction of Hepatic Hyperplasia in the Rat," August 25, 1972: 461) reports on an experiment in which each of five groups consisting of six rats was put on a diet with a different carbohydrate. At the conclusion
It is common practice in many countries to destroy (shred) refrigerators at the end of their useful lives. In this process material from insulating foam may be released into the atmosphere. The article "Release of Fluorocarbons from Insulation Foam in Home Appliances During Shredding" (J. of the
Refer to Exercise 38. An article in the British scientific journal Nature ("Sucrose Induction of Hepatic Hyperplasia in the Rat," August 25, 1972: 461) reports on an experiment in which each of five groups consisting of six rats was put on a diet with a different carbohydrate. At the conclusion of
Four laboratories (1-4) are randomly selected from a large population, and each is asked to make three determinations of the percentage of methyl alcohol in specimens of a compound taken from a single batch. Based on the accompanying data, are differences among laboratories a source of variation in
The critical flicker frequency (cff) is the highest frequency (in cycles/sec) at which a person can detect the flicker in a flickering light source. At frequencies above the cff, the light source appears to be continuous even though it is actually flickering. An investigation carried out to see
Let c1, c2,..., cI be numbers satisfying (ci = 0. Then (ciµi = c1µ1 + ...+ cIµI is called a contrast in the µi's. Notice that with c1 = 1, c2 = -1, c3 =... = cI = 0, (ciµi = µ1 - µ2 which implies that every pair-wise difference between µi's is a contrast (so is, e.g., µ1 - .5µ2 - .5µ3).
Four types of mortars-ordinary cement mortar (OCM), polymer impregnated mortar (PIM), resin mortar (RM), and polymer cement mortar (PCM)-were subjected to a compression test to measure strength (MPa). Three strength observations for each mortar type are given in the article "Polymer Mortar
Suppose the xij's are "coded" by yij = cxij + d. How does the value of the F statistic computed from the yij's compare to the value computed from the xij's? Justify your assertion.
In Example 10.11, subtract x̅i. from each observation in the ith sample (i = 1, ..., 6) to obtain a set of 18 residuals. Then construct a normal probability plot and comment on the plausibility of the normality assumption.
Consider the following summary data on the modulus of elasticity (Ã— 106 psi) for lumber of three different grades [in close agreement with values in the article "Bending Strength and Stiffness of Second-Growth Douglas-Fir Dimension Lumber" (Forest Products J., 1991: 35-43), except that
The article "Origin of Precambrian Iron Formations" (Econ. Geology, 1964: 1025-1057) reports the following data on total Fe for four types of iron formation (1 = carbonate, 2 = silicate, 3 = magnetite, 4 = hematite).Carry out an analysis of variance F test at significance level .01, and summarize
An experiment was carried out to compare electrical resistivity for six different low-permeability concrete bridge deck mixtures. There were 26 measurements on concrete cylinders for each mixture; these were obtained 28 days after casting. The entries in the accompanying ANOVA table are based on
A study of the properties of metal plate-connected trusses used for roof support ("Modeling Joints Made with Light-Gauge Metal Connector Plates," Forest Products J., 1979: 39-44) yielded the following observations on axial-stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in: 4:
Six samples of each of four types of cereal grain grown in a certain region were analyzed to determine thiamin content, resulting in the following data (mg/g):Does this data suggest that at least two of the grains differ with respect to true average thiamin content? Use a level a = .05 test.
An experiment was carried out to investigate the effect of species (factor A, with I = 4) and grade (factor B, with J = 3) on breaking strength of wood specimens. One observation was made for each species-grade combination- resulting in SSA = 442.0, SSB = 428.6, and SSE = 123.4. Assume that an
The strength of concrete used in commercial construction tends to vary from one batch to another. Consequently, small test cylinders of concrete sampled from a batch are "cured" for periods up to about 28 days in temperature and moisture-controlled environments before strength measurements are
For the data of Example 11.5, check the plausibility of assumptions by constructing a normal probability plot of the residuals and a plot of the residuals versus the predicted values, and comment on what you learn?
Suppose that in the experiment described in Exercise 6 the five houses had actually been selected at random from among those of a certain age and size, so that factor B is random rather than fixed. Test H0: (2B = 0 versus Ha: (2B > 0 using a level .01 test?
a. Show that a constant d can be added to (or subtracted from) each xij without affecting any of the ANOVA sums of squares. b. Suppose that each xij is multiplied by a nonzero constant. c. How does this affect the ANOVA sums of squares? How does this affect the values of the F statistics FA and FB?
Use the fact that E(Xij) = µ + ai + βj with (ai = (βj = 0 to show that E(X̅i. - X̅..) = αi, so that = X̅i. - X̅.. is an unbiased estimator for ai.
The power curves of Figures 10.5 and 10.6 can be used to obtain β = P(type II error) for the F test in two-factor ANOVA. For fixed values of a1, a2, ... , a1, the quantity (2 = (J/I) (α2i / (2 is computed. Then the figure corresponding to v1 = I - 1 is entered on the horizontal axis at the value
In an experiment to assess the effects of curing time (factor A) and type of mix (factor B) on the compressive strength of hardened cement cubes, three different curing times were used in combination with four different mixes, with three observations obtained for each of the 12 curing time-mix
The article "Towards Improving the Properties of Plaster Moulds and Castings" (J. Engr. Manuf., 1991: 265-269) describes several ANOVAs carried out to study how the amount of carbon fiber and sand additions affect various characteristics of the molding process. Here we give data on casting hardness
The accompanying data resulted from an experiment to investigate whether yield from a certain chemical process depended either on the formulation of a particular input or on mixer speed.A statistical computer package gave SS(Form) = 2253.44, SS(Speed) = 230.81, SS(Form*Speed) = 18.58, and SSE =
A two-way ANOVA was carried out to assess the impact of type of farm (government agricultural settlement, established, individual) and tractor maintenance method (preventive, predictive, running, corrective, overhauling, breakdown) on the response variable maintenance practice contribution. There
Four different coatings are being considered for corrosion protection of metal pipe. The pipe will be buried in three different types of soil. To investigate whether the amount of corrosion depends either on the coating or on the type of soil, 12 pieces of pipe are selected. Each piece is coated
The article "Fatigue Limits of Enamel Bonds with Moist and Dry Techniques" (Dental Materials, 2009: 1527-1531) described an experiment to investigate the ability of adhesive systems to bond to mineralized tooth structures. The response variable is shear bond strength (MPa), and two different
In an experiment to investigate the effect of "cement factor" (number of sacks of cement per cubic yard) on flexural strength of the resulting concrete ("Studies of Flexural Strength of Concrete. Part 3: Effects of Variation in Testing Procedure," Proceedings, ASTM, 1957: 1127-1139), I = 3
A study was carried out to compare the writing lifetimes of four premium brands of pens. It was thought that the writing surface might affect lifetime, so three different surfaces were randomly selected. A writing machine was used to ensure that conditions were otherwise homogeneous (e.g., constant
The accompanying data was obtained in an experiment to investigate whether compressive strength of concrete cylinders depends on the type of capping material used or variability in different batches ("The Effect of Type of Capping Material on the Compressive Strength of Concrete Cylinders,"
a. Show that E(X̅i.. - X̅...) = αi, so that X̅i.. - X̅.. is an unbiased estimator for αi (in the fixed effects model). b. With ij = X̅ij.. - X̅i.. - X̅.j. + X̅..., show that ij is an unbiased estimator for γij (in the fixed effects model)?
Show how a 100 (1 - α) % t CI for αi - αi can be obtained. Then compute a 95% interval for α2 - α3 using the data from Exercise 19?
When both factors are random in a two-way ANOVA experiment with K replications per combination of factor levels, the expected mean squares are E(MSE) =(2, EMSA) = (2 + K(2G + JK(2A, E(MSB) = (2 + K(2G + IK(2B, and E(MSAB) = (2 + K(2G.a. What F ratio is appropriate for testing H0G: (2G = 0 versus
The output of a continuous extruding machine that coats steel pipe with plastic was studied as a function of the thermostat temperature profile (A, at three levels), the type of plastic (B, at three levels), and the speed of the rotating screw that forces the plastic through a tube forming die (C,
To see whether thrust force in drilling is affected by drilling speed (A), feed rate (B), or material used (C), an experiment using four speeds, three rates, and two materials was performed, with two samples (L = 2) drilled at each combination of levels of the three factors. Sums of squares were
The article "Effects of Household Fabric Softeners on Thermal Comfort of Cotton and PolyesterFabrics After Repeated Launderings" (Family and Consumer Science Research J., 2009: 535-549) reported the results of a three-factor ANOVA carried out to investigate the impact of fabric softener treatment
An investigation of the machinability of beryllium-copper alloy using two different dielectric mediums and four different working currents resulted in the following data on material removal rate (this is a subset of the data that appeared in the article "Statistical Analysis and Optimization Study
The following summary quantities were computed from an experiment involving four levels of nitrogen (A), two times of planting (B), and two levels of potassium (C) ("Use and Misuse of Multiple Comparison Procedures," Agronomy J., 1977: 205-208). Only one observation (N content, in percentage, of
Nickel titanium (NiTi) shape memory alloy (SMA) has been widely used in medical devices. This is attributable largely to the alloy's shape memory effect (material returns to its original shape after heat deformation), super elasticity, and biocompatibility. An alloy element is usually coated on the
When factors A and B are fixed but factor C is random and the restricted model is used (see the footnote on page 438; there is a technical complication with the unrestricted model here), and E(MSE) = (2.E(MSA) = (2 + JL(2AC + JKL / I - 1 (Î±2iE(MSB) = (2 + JL(2BC + IKL / J - 1 (Î²2jE(MSC) = (2
Because of potential variability in aging due to different castings and segments on the castings, a Latin square design with N = 7 was used to investigate the effect of heat treatment on aging. With A = castings, B = segments, C = heat treatments, summary statistics include x... = 3815.8, (x2i.. =
The article "The Responsiveness of Food Sales to Shelf Space Requirements" (J. Marketing Research, 1964: 63-67) reports the use of a Latin square design to investigate the effect of shelf space on food sales. The experiment was carried out over a 6-week period using six different stores, resulting
The article "Variation in Moisture and Ascorbic Acid Content from Leaf to Leaf and Plant to Plant in Turnip Greens" (Southern Cooperative Services Bull., 1951: 13-17) uses a Latin square design in which factor A is plant, factor B is leaf size (smallest to largest), factor C (in parentheses) is
The article "An Assessment of the Effects of Treatment, Time, and Heat on the Removal of Erasable Pen Marks from Cotton and Cotton/Polyester Blend Fabrics (J. of Testing and Eval., 1991: 394-397) reports the following sums of squares for the response variable degree of removal of marks: SSA =
A four-factor ANOVA experiment was carried out to investigate the effects of fabric (A), type of exposure (B), level of exposure (C), and fabric direction (D) on extent of color change in exposed fabric as measured by a spectrocolorimeter. Two observations were made for each of the three fabrics,
The accompanying data resulted from an experiment to study the nature of dependence of welding current on three factors: welding voltage, wire feed speed, and tip-to-work-piece distance. There were two levels of each factor (a 23 experiment) with two replications per combination of levels (the
The accompanying data resulted from a 23 experiment with three replications per combination of treatments designed to study the effects of concentration of detergent (A), concentration of sodium carbonate (B), and concentration of sodium carboxymethyl cellulose (C) on the cleaning ability of a
In an experiment to see whether the amount of coverage of light-blue interior latex paint depends either on the brand of paint or on the brand of roller used, one gallon of each of four brands of paint was applied using each of three brands of roller, resulting in the following data (number of
In a study of processes used to remove impurities from cellulose goods ("Optimization of Rope-Range Bleaching of Cellulosic Fabrics," Textile Research J., 1976: 493-496), the following data resulted from a 24 experiment involving the desizing process. The four factors were enzyme concentration (A),
As with many dried products, sun-dried tomatoes can exhibit an undesirable discoloration during the drying and storage process. A replicated 23 experiment was conducted in an effort to relate color quality to the factors storage time, temperature, and packaging type ("Use of Factorial Experimental
The following data on power consumption in electric furnace heats (kW consumed per ton of melted product) resulted from a 24 factorial experiment with three replicates ("Studies on a 10-cwt Arc Furnace," J. of the Iron and Steel Institute, 1956: 22). The factors were nature of roof (A, low/high),
The article "Statistical Design and Analysis of Qualification Test Program for a Small Rocket Engine" (Industrial Quality Control, 1964: 14-18) presents data from an experiment to assess the effects of vibration (A), temperature cycling (B), altitude cycling (C), and temperature for altitude
a. In a 24 experiment, suppose two blocks are to be used, and it is decided to confound the ABCD interaction with the block effect. Which treatments should be carried out in the first block [the one containing the treatment (1)], and which treatments are allocated to the second block?b. In an
a. An experiment was carried out to investigate the effects on audio sensitivity of varying resistance (A), two capacitances (B, C), and inductance of a coil (D) in part of a television circuit. If four blocks were used with four treatments per block and the defining effects for confounding were AB
In an experiment involving four factors (A, B, C, and D) and four blocks, show that at least one main effect or two-factor interaction effect must be confounded with the block effect?
a. In a seven-factor experiment (A,..., G), suppose a quarter-replicate is actually carried out. If the defining effects are ABCDE and CDEFG, what is the third non-estimable effect, and what treatments are in the group containing (1)? What are the alias groups of the seven main effects? b. If the
The article "Applying Design of Experiments to Improve a Laser Welding Process" (J. of Engr. Manufacture, 2008: 1035-1042) included the results of a half replicate of a 24 experiment. The four factors were: A. Power (2900 W, 3300 W), B. Current (2400 mV,3600 mV), C. Laterals cleaning (No, Yes), and
A half-replicate of a 25 experiment to investigate the effects of heating time (A), quenching time (B), drawing time (C), position of heating coils (D), and measurement position (E) on the hardness of steel castings resulted in the accompanying data. Construct the ANOVA table, and (assuming second
In an experiment to assess the effect of the angle of pull on the force required to cause separation in electrical connectors, four different angles (factor A) were used, and each of a sample of five connectors (factor B) was pulled once at each angle ("A Mixed Model Factorial Experiment in Testing
The results of a study on the effectiveness of line drying on the smoothness of fabric were summarized in the article "Line-Dried vs. Machine-Dried Fabrics: Comparison of Appearance, Hand, and Consumer Acceptance" (Home Econ. Research J., 1984: 27-35). Smoothness scores were given for nine
The water absorption of two types of mortar used to repair damaged cement was discussed in the article "Polymer Mortar Composite Matrices for Maintenance-Free, Highly Durable Ferrocement" (J. of Ferrocement, 1984: 337-345). Specimens of ordinary cement mortar (OCM) and polymer cement mortar (PCM)
Four plots were available for an experiment to compare clover accumulation for four different sowing rates ("Performance of Overdrilled Red Clover with Different Sowing Rates and Initial Grazing Managements," N. Zeal. J. of Exp. Ag., 1984: 71-81). Since the four plots had been grazed differently
In an automated chemical coating process, the speed with which objects on a conveyor belt are passed through a chemical spray (belt speed), the amount of chemical sprayed (spray volume), and the brand of chemical used (brand) are factors that may affect the uniformity of the coating applied. A
Coal-fired power plants used in the electrical industry have gained increased public attention because of the environmental problems associated with solid wastes generated by large-scale combustion ("Fly Ash Binders in Stabilization of FGD Wastes," J. of Environmental Engineering, 1998: 43-49). A
Impurities in the form of iron oxides lower the economic value and usefulness of industrial minerals, such as kaolins, to ceramic and paper-processing industries. A 24 experiment was conducted to assess the effects of four factors on the percentage of iron removed from kaolin samples ("Factorial
Factorial designs have been used in forestry to assess the effects of various factors on the growth behavior of trees. In one such experiment, researchers thought that healthy spruce seedlings should bud sooner than diseased spruce seedlings ("Practical Analysis of Factorial Experiments in
One property of automobile air bags that contributes to their ability to absorb energy is the permeability (ft3/ft2/ min) of the woven material used to construct the air bags. Understanding how permeability is influenced by various factors is important for increasing the effectiveness of air bags.
A chemical engineer has carried out an experiment to study the effects of the fixed factors of vat pressure (A), cooking time of pulp (B), and hardwood concentration (C) on he strength of paper. The experiment involved two pressures, four cooking times, three concentrations, and two observations at
The bond strength when mounting an integrated circuit on a metalized glass substrate was studied as a function of factor A = adhesive type, factor B = curve time, and factor C = conductor material (copper and nickel). The data follows, along with an ANOVA table from Minitab. What conclusions can
A particular county employs three assessors who are responsible for determining the value of residential property in the county. To see whether these assessors differ systematically in their assessments, 5 houses are selected, and each assessor is asked to determine the market value of each house.
The article "Effect of Cutting Conditions on Tool Performance in CBN Hard Turning" (J. of Manuf. Processes, 2005: 10-17) reported the accompanying data on cutting speed (m/s), feed (mm/rev), depth of cut (mm), and tool life (min). Carry out a three-factor ANOVA on tool life, assuming the absence of
Analogous to a Latin square, a Greco-Latin square design can be used when it is suspected that three extraneous factors may affect the response variable and all four factors (the three extraneous ones and the one of interest) have the same number of levels. In a Latin square, each level of the
The accompanying data resulted from an experiment involving three different brands of lathe in combination with three different operators (the blocking factor). The response variable is the percentage of acceptable product produced during a full workday shift (from "A Software- Based Resource
The paper "Exercise Thermoregulation and Hyperprolac-tinaemia" (Ergonomics, 2005: 1547-1557) discussed how various aspects of exercise capacity might depend on the temperature of the environment. The accompanying data on body mass loss (kg) after exercising on a semi-recumbent cycle ergometer in
The article "The Effects of a Pneumatic Stool and a One-Legged Stool on Lower Limb Joint Load and Muscular Activity During Sitting and Rising" (Ergonomics, 1993: 519-535) gives the accompanying data on the effort required of a subject to arise from four different types of stools (Borg scale).
The efficiency ratio for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). The article "Statistical Process Control of a Phosphate Coating Line" (Wire J. Intl., May 1997: 78-81) gave the accompanying data on tank
Suppose the expected cost of a production run is related to the size of the run by the equation y = 4000 + 10x. Let Y denote an observation on the cost of a run. If the 1ariables' size and cost are related according to the simple linear regression model, could it be the case that P(Y > 5500 when x
Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 5.00 - .01x and ( = .075. a. What is the expected change in reaction time for a
Refer back to the data in Exercise 4, in which y = ammonium concentration (mg/L) and x = transpiration (ml/h). Summary quantities include n = 13, (xi = 303.7, (yi = 52.8, Sxx = 1585.230769, Sxy = −341.959231, and Syy = 77.270769. a. Obtain the equation of the estimated regression line and use it
The accompanying data on x = current density (mAycm2) and y = rate of deposition smmymin d appeared in the article "Plating of 60/40 Tin/Lead Solder for Head Termination Metallurgy" (Plating and Surface Finishing, Jan. 1997: 38-40). Do you agree with the claim by the article's author that "a linear
Refer to the tank temperature-efficiency ratio data given in Exercise 1. a. Determine the equation of the estimated regression line. b. Calculate a point estimate for true average efficiency ratio when tank temperature is 182. c. Calculate the values of the residuals from the least squares line for
Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were determined for a sample of concrete beams of a certain type,
The article "Characterization of Highway Runoff in Austin, Texas, Area" (J. of Envir. Engr., 1998: 131-137) gave a scatter-plot, along with the least squares line, of x = rain-full volume (m3) and y = runoff volume (m3) for a particular location. The accompanying values were read from the plot.a.
No-fines concrete, made from a uniformly graded coarse aggregate and a cement-water paste, is beneficial in areas prone to excessive rainfall because of its excellent drainage properties. The article "Pavement Thickness Design for No-Fines Concrete Parking Lots," J. of Trans. Engr., 1995: 476-484)
For the past decade, rubber powder has been used in asphalt cement to improve performance. The article "Experimental Study of Recycled Rubber-Filled High-Strength Concrete" (Magazine of Concrete Res., 2009: 549-556) includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based
The following data is representative of that reported in the article "An Experimental Correlation of Oxides of Nitrogen Emissions from Power Boilers Based on Field Data" (J. of Engr. for Power, July 1973: 165-170), with x = burner-area liberation rate (MBtuyhr-ft2) and y = NOx emission rate
The article "Exhaust Emissions from Four-Stroke Lawn Mower Engines" (J. of the Air and Water Mgmnt. Assoc., 1997: 945-952) reported data from a study in which both a baseline gasoline mixture and a reformulated gasoline were used. Consider the following observations on age (yr) and NOx emissions
The bond behavior of reinforcing bars is an important determinant of strength and stability. The article "Experimental Study on the Bond Behavior of Reinforcing Bars Embedded in Concrete Subjected to Lateral Pressure" (J. of Materials in Civil Engr., 2012: 125-133) reported the results of one
Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of cross-linked cotton fabric. An increase in the degree of cross-linking, as determined by ester carboxyl band absorbence, improves the wrinkle resistance of the fabric (at the
Calcium phosphate cement is gaining increasing attention for use in bone repair applications. The article "Short-Fibre Reinforcement of Calcium Phosphate Bone Cement" (J. of Engr. in Med., 2007: 203-211) reported on a study in which polypropylene fibers were used in an attempt to improve fracture
a. Obtain SSE for the data in Exercise 19 from the defining formula [SSE = ((yi - i)2], and compare to the value calculated from the computational formula. b. Calculate the value of total sum of squares. Does the simple linear regression model appear to do an effective job of explaining variation
The invasive diatom species Didymosphenia geminate has the potential to inflict substantial ecological and economic damage in rivers. The article "Substrate Characteristics Affect Colonization by the Bloom-Forming Diatom Didymosphenia geminata (Aquatic Ecology, 2010: 33-40) described an
Show that b1 and b0 of expressions (12.2) and (12.3) satisfy the normal equations?
Show that the "point of averages" (x̅, y̅) lies on the estimated regression line?
Suppose an investigator has data on the amount of shelf space x devoted to display of a particular product and sales revenue y for that product. The investigator may wish to fit a model for which the true regression line passes through (0, 0). The appropriate model is Y = β1x + ε. Assume that
a. Consider the data in Exercise 20. Suppose that instead of the least squares line passing through the points (x1, y1),..., (xn, yn), we wish the least squares line passing through (x1 x2, y1) ,..., (xn - x̅, yn). Construct a scatter-plot of the (xi, yi) points and then of the (xi - x̅, yi)
Consider the following three data sets, in which the variables of interest are x = commuting distance and y = commuting time. Based on a scatter-plot and the values of s and r2, in which situation would simple linear regression be most (least) effective, and why?
Bivariate data often arises from the use of two different techniques to measure the same quantity. As an example, the accompanying observations on x = hydrogen concentration1(ppm) using a gas chromatography method and y = concentration using a new sensor method were read from a graph in the article

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