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applied statistics and probability for engineers

Probability And Statistics For Engineering And The Sciences 7th Edition Dave Ellis, Jay L Devore - Solutions

A modification has been made to the process for producing a certain type of “time-zero” film (film that begins to develop as soon as a picture is taken). Because the modification involves extra cost, it will be incorporated only if sample data strongly indicates that the modification has
The article “A Study of Wood Stove Particulate Emissions”(J. Air Pollution Control Assn., 1979: 724–728) reports the following data on burn time (hours) for samples of oak and pine. Test at level .05 to see whether there is any difference in true average burn time for the two types of wood.
Suppose that observations X1, X2, . . . , Xn are made on a process at times 1, 2, . . . , n. On the basis of this data, we wish to test H0: the Xis constitute an independent and identically distributed sequence versus Ha: Xi1 tends to be larger than Xi for i 1, . . . , n(an increasing
The accompanying 25 observations on fracture toughness of base plate of 18% nickel maraging steel were reported in the article “Fracture Testing of Weldments” (ASTM Special Publ. No. 381, 1965: 328–356). Suppose a company will agree to purchase this steel for a particular application only if
Use the large-sample version of the Wilcoxon test at significance level .05 on the data of Exercise 37 in Section 9.3 to decide whether the true mean difference between outdoor and indoor concentrations exceeds .20.
Reconsider the situation described in Exercise 41 of Section 9.3, and use the Wilcoxon test to test the appropriate hypotheses.
A random sample of 15 automobile mechanics certified to work on a certain type of car was selected, and the time (in minutes) necessary for each one to diagnose a particular problem was determined, resulting in the following data:30.6 30.1 15.6 26.7 27.1 25.4 35.0 30.8 31.9 53.2 12.5 23.2 8.8 24.9
The accompanying data is a subset of the data reported in the article “Synovial Fluid pH, Lactate, Oxygen and Carbon Dioxide Partial Pressure in Various Joint Diseases” (Arthritis and Rheumatism, 1971: 476–477). The observations are pH values of synovial fluid (which lubricates joints and
Use the Wilcoxon test to analyze the data given in Example 8.9.
Reconsider the situation described in Exercise 32 of Section 8.2, and use the Wilcoxon test with .05 to test the relevant hypotheses.
Suppose that in Exercise 32 each student had been categorized with respect to political views, marijuana usage, and religious preference, with the categories of this latter factor being Protestant, Catholic, and other. The data could be displayed in three different two-way tables, one corresponding
Each individual in a random sample of high school and college students was cross-classified with respect to both political views and marijuana usage, resulting in the data displayed in the accompanying two-way table (“Attitudes About Marijuana and Political Views,” Psychological Reports, 1973:
A random sample of individuals who drive alone to work in a large metropolitan area was obtained, and each individual was categorized with respect to both size of car and commuting distance. Does the accompanying data suggest that commuting distance and size of car are related in the population
The accompanying data on sex combinations of two recombinants resulting from six different male genotypes appears in the article “A New Method for Distinguishing Between Meiotic and Premeiotic Recombinational Events in Drosophila melanogaster” (Genetics, 1979: 543–554). Does the data support
The article “Susceptibility of Mice to Audiogenic Seizure Is Increased by Handling Their Dams During Gestation”(Science, 1976: 427–428) reports on research into the effect of different injection treatments on the frequencies of audiogenic seizures.Treatment 21 15 714 24 20 44 54 No Response
The article “Human Lateralization from Head to Foot:Sex-Related Factors” (Science, 1978: 1291–1292) reports for both a sample of right-handed men and a sample of right-handed women the number of individuals whose feet were the same size, had a bigger left than right foot (a difference of half
The following data resulted from an experiment to study the effects of leaf removal on the ability of fruit of a certain type to mature (“Fruit Set, Herbivory, Fruit Reproduction, and the Fruiting Strategy of Catalpa speciosa,” Ecology, 1980:57–64):Does the data suggest that the chance of a
Consider the accompanying 2 3 table displaying the sample proportions that fell in the various combinations of categories (e.g., 13% of those in the sample were in the first category of both factors).a. Suppose the sample consisted of n 100 people. Use the chi-squared test for independence with
The results of an experiment to assess the effect of crude oil on fish parasites are described in the article “Effects of Crude Oils on the Gastrointestinal Parasites of Two Species of Marine Fish” (J. Wildlife Diseases, 1983: 253–258).Three treatments (corresponding to populations in the
Have you ever wondered whether soccer players suffer adverse effects from hitting “headers”? The authors of the article “No Evidence of Impaired Neurocognitive Performance in Collegiate Soccer Players” (The Amer. J. of Sports Medicine, 2002: 157–162) investigated this issue from several
The NCAA basketball tournament begins with 64 teams that are apportioned into four regional tournaments, each involving 16 teams. The 16 teams in each region are then ranked (seeded) from 1 to 16. During the 12-year period from 1991 to 2002, the top-ranked team won its regional tournament 22 times,
Let p1 denote the proportion of successes in a particular population. The test statistic value in Chapter 8 for testing
The authors of the article “Predicting Professional Sports Game Outcomes from Intermediate Game Scores” (Chance, 1992: 18–22) used a chi-squared test to determine whether there was any merit to the idea that basketball games are not settled until the last quarter, whereas baseball games are
Qualifications of male and female head and assistant college athletic coaches were compared in the article “Sex Bias and the Validity of Believed Differences Between Male and Female Interscholastic Athletic Coaches” (Research Quarterly for Exercise and Sport, 1990: 259–267). Each person in
In a sample of 91 college soccer players, the mean number of concussions was 1.07, and the standard deviation was 1.83(“No Evidence of Impaired Neurocognitive Performance in Collegiate Soccer Players,” The Amer. J. of Sports Med., 2002: 157–162). Information was also collected for a sample of
The accompanying data refers to leaf marks found on white clover samples selected from both long-grass areas and short-grass areas (“The Biology of the Leaf Mark Polymorphism in Trifolium repens L.,” Heredity, 1976:306–325). Use a 2 test to decide whether the true proportions of different
a. Show that another expression for the chi-squared statistic is 2 k i1n Npi 2i 0 n Why is it more efficient to compute 2 using this formula?b. When the null hypothesis is H0: p1 p2 pk 1/k(i.e., pi0 1/k for all i), how does the formula of part (a)simplify? Use the simplified
Criminologists have long debated whether there is a relationship between weather conditions and the incidence of violent crime. The author of the article “Is There a Season for Homicide?” (Criminology, 1988: 287–296) classified 1361 homicides according to season, resulting in the accompanying
Sorghum is an important cereal crop whose quality and appearance could be affected by the presence of pigments in the pericarp (the walls of the plant ovary). The article“A Genetic and Biochemical Study on Pericarp Pigments in a Cross Between Two Cultivars of Grain Sorghum, Sorghum Bicolor”
An information retrieval system has ten storage locations.Information has been stored with the expectation that the long-run proportion of requests for location i is given by pi (5.5 ⏐i 5.5⏐)/30. A sample of 200 retrieval requests gave the following frequencies for locations 1–10,
It is hypothesized that when homing pigeons are disoriented in a certain manner, they will exhibit no preference for any direction of flight after takeoff (so that the direction X should be uniformly distributed on the interval from 0° to 360°). To test this, 120 pigeons are disoriented, let
A statistics department at a large university maintains a tutoring service for students in its introductory service courses. The service has been staffed with the expectation that 40% of its clients would be from the business statistics course, 30% from engineering statistics, 20% from the
a. Having obtained a random sample from a population, you wish to use a chi-squared test to decide whether the population distribution is standard normal. If you base the test on six class intervals having equal probability under H0, what should be the class intervals?b. If you wish to use a
A study of sterility in the fruit fly (“Hybrid Dysgenesis in Drosophila melanogaster: The Biology of Female and Male Sterility,” Genetics, 1979: 161–174) reports the following data on the number of ovaries developed for each female fly in a sample of size 1388. One model for unilateral
The article “Feeding Ecology of the Red-Eyed Vireo and Associated Foliage-Gleaning Birds” (Ecological Monographs, 1971: 129–152) presents the accompanying data on the variable X the number of hops before the first flight and preceded by a flight. The author then proposed and fit a geometric
The following data set consists of 25 observations on fracture toughness of base plate of 18% nickel maraging steel(from “Fracture Testing of Weldments,” ASTM Special Publ.No. 381, 1965: 328–356). Use the normal probability plot correlation coefficient test to decide whether a normal
The article “Compatibility of Outer and Fusible Interlining Fabrics in Tailored Garments (Textile Res. J., 1997:137–142) gave the following observations on bending rigidity (N m) for medium-quality fabric specimens, from which the accompanying MINITAB output was obtained:
Each headlight on an automobile undergoing an annual vehicle inspection can be focused either too high (H), too low (L), or properly (N). Checking the two headlights simultaneously (and not distinguishing between left and right)results in the six possible outcomes HH, LL, NN, HL, HN, and LN. If the
The article “A Probabilistic Analysis of Dissolved Oxygen–Biochemical Oxygen Demand Relationship in Streams”(J. Water Resources Control Fed., 1969: 73–90) reports data on the rate of oxygenation in streams at 20°C in a certain region. The sample mean and standard deviation were computed as
An article in Annals of Mathematical Statistics reports the following data on the number of borers in each of 120 groups of borers. Does the Poisson pmf provide a plausible model for the distribution of the number of borers in a group?[Hint: Add the frequencies for 7, 8, . . . , 12 to establish a
A certain type of flashlight is sold with the four batteries included. A random sample of 150 flashlights is obtained, and the number of defective batteries in each is determined, resulting in the following data:Let X be the number of defective batteries in a randomly selected flashlight. Test the
Say as much as you can about the P-value for an upper-tailed chi-squared test in each of the following situations:a. 2 7.5, df 2b. 2 13.0, df 6c. 2 18.0, df 9d. 2 21.3, k 5e. 2 5.0, k 4
What conclusion would be appropriate for an upper-tailed chi-squared test in each of the following situations?a. .05, df 4, 2 12.25b. .01, df 3, 2 8.54c. .10, df 2, 2 4.36d. .01, k 6, 2 10.20
Show that the chi-squared statistic for the test of independence can be written in the form 2 I i1J j1 n Why is this formula more efficient computationally than the defining formula for 2?
A sample of n 20 companies was selected, and the values of y stock price and k 15 predictor variables (such as quarterly dividend, previous year’s earnings, and debt ratio)were determined. When the multiple regression model using these 15 predictors was fit to the data, R2 .90 resulted.
The article “A Statistical Analysis of the Notch Toughness of 9% Nickel Steels Obtained from Production Heats” (J. of Testing and Eval., 1987: 355–363) reports on the results of a multiple regression analysis relating Charpy v-notch toughness y (joules) to the following variables: x1 plate
A study was carried out to relate time to failure (y) of a certain machine component to the variables operating voltage(x1), motor speed (x2), and operating temperature (x3). The resulting data set consisted of n 20 observations. When the model with the three variables x1, x2, and x3 was fit to
A multiple regression analysis was carried out to relate y tensile strength of a synthetic-fiber specimen to the variables x1 percent cotton and x2 drying time. The data set consisted of n 12 observations.a. The estimated coefficients were ˆ0 180.00, ˆ1 1.000, and ˆ2 10.500.
The article “Chemithermomechanical Pulp from Mixed High Density Hardwoods” (TAPPI, July 1988: 145–146)reports on a study in which the accompanying data was obtained to relate y specific surface area (cm3/g) to x1 %NaOH used as a pretreatment chemical and x2 treatment time (min) for a
The effect of manganese (Mn) on wheat growth is examined in the article “Manganese Deficiency and Toxicity Effects on Growth, Development and Nutrient Composition in Wheat” (Agronomy J., 1984: 213–217). A quadratic regression model was used to relate y plant height (cm) to x log10(added
Conductivity is one important characteristic of glass. The article “Structure and Properties of Rapidly Quenched Li2O-Al2O-Nb2O5 Glasses” (J. Amer. Ceramic Soc., 1983:890–892) reports the accompanying data on x Li2O content of a certain type of glass and y conductivity at 500 K.x | 19 20
The accompanying data on x frequency (MHz) and y output power (W) for a certain laser configuration was read from a graph in the article “Frequency Dependence in RF Discharge Excited Waveguide CO2 Lasers” (IEEE J.Quantum Electronics, 1984: 509–514).x | 60 63 77 100 125 157 186 222 y | 16
The article “An Experimental Study of Resistance Spot Welding in 1 mm Thick Sheet of Low Carbon Steel” (J. of Engr. Manufacture, 1996: 341–348) discussed a statistical analysis whose basic aim was to establish a relationship that could explain the variation in weld strength (y) by relating
An ammonia bath is the one most widely used for depositing Pd-Ni alloy coatings. The article “Modelling of Palladium and Nickel in an Ammonia Bath in a Rotary Device” (Plating and Surface Finishing, 1997: 102–104)reported on an investigation into how bath composition characteristics affect
An aeronautical engineering student carried out an experiment to study how y lift/drag ratio related to the variables x1 position of a certain forward lifting surface relative to the main wing and x2 tail placement relative to the main wing, obtaining the following data (Statistics for
Air pressure (psi) and temperature (°F) were measured for a compression process in a certain piston-cylinder device, resulting in the following data (from Introduction to Engineering Experimentation, Prentice-Hall, Inc., 1996, p. 153):Pressure 20.0 40.4 60.8 80.2 100.4 Temperature 44.9 102.4 142.3
Feature recognition from surface models of complicated parts is becoming increasingly important in the development of efficient computer-aided design (CAD) systems.The article “A Computationally Efficient Approach to Feature Abstraction in Design-Manufacturing Integration”(J. of Engr. for
The authors of the article “Long-Term Effects of Cathodic Protection on Prestressed Concrete Structures” (Corrosion, 1997: 891–908) presented a scatter plot of y steady-state permeation flux ( A/cm2) versus x inverse foil thickness(cm1); the substantial linear pattern was used as a basis
Curing concrete is known to be vulnerable to shock vibrations, which may cause cracking or hidden damage to the material. As part of a study of vibration phenomena, the paper “Shock Vibration Test of Concrete” (ACI Materials J., 2002: 361–370) reported the accompanying data on peak particle
Refer to the water-discharge data given in Exercise 55 and let y ln(q), x1 ln(a), and x2 ln(b). Consider fitting the model Y 0 1x1 2x2 !.a. The resulting hiis are .138, .302, .266, .604, .464, .360,.215, .153, .214, and .284. Does any observation appear to be influential?b. The estimated
Multiple regression output from MINITAB for the PAH data of Exercise 53 in the previous section included the following information:Unusual Observations Obs x1 flth Fit SE Fit Residual St Resid 6 243500 604.7 582.9 40.7 21.8 1.25X 7 67793 27.7 139.3 12.3 111.6 2.62R R denotes an observation with a
A study carried out to investigate the relationship between a response variable relating to pressure drops in a screen-plate bubble column and the predictors x1 superficial fluid velocity, x2 liquid viscosity, and x3 opening mesh size resulted in the accompanying data (“A Correlation of?
Reconsider the wood specific gravity data referred to in Exercise 56. The following R2 values resulted from regressing each predictor on the other four predictors (in the first regression, the dependent variable was x1 and the predictors were x2–x5, etc.): .628, .711, .341, .403, and .403. Does
The accompanying MINITAB output resulted from applying both the backward elimination method and the forward selection method to the wood specific gravity data referred to in Exercise 56. For each method, explain what occurred at every iteration of the algorithm.Response is spgrav on 5 predictors,
MINITAB’s Best Regression option was used on the wood specific gravity data referred to in Exercise 56, resulting in the accompanying output. Which model(s) would you recommend investigating in more detail?Response is spgrav s %s p s s su r u p pm n m r ll g r w tt f f o aa R-Sq i i o bb Vars
The article “Creep and Fatigue Characteristics of Ferrocement Slabs” (J. Ferrocement, 1984: 309–322) reported data on y tensile strength (MPa), x1 slab thickness (cm), x2 load(kg), x3 age at loading (days), and x4 time under test(days) resulting from stress tests of n 9 reinforced
In the accompanying table, we give the smallest SSE for each number of predictors k (k 1, 2, 3, 4) for a regression problem in which y cumulative heat of hardening in cement, x1 % tricalcium aluminate, x2 % tricalcium silicate, x3 % aluminum ferrate, and x4 % dicalcium silicate.Number
In an experiment to study factors influencing wood specific gravity (“Anatomical Factors Influencing Wood Specific Gravity of Slash Pines and the Implications for the Development of a High-Quality Pulpwood,” TAPPI, 1964:401–404), a sample of 20 mature wood samples was obtained, and
The article “Bank Full Discharge of Rivers” (Water Resources J., 1978: 1141–1154) reports data on discharge amount (q, in m3/sec), flow area (a, in m2), and slope of the water surface (b, in m/m) obtained at a number of floodplain stations. A subset of the data follows. The article proposed a
The accompanying data resulted from a study of the relationship between brightness of finished paper (y) and the variables H2O2% by weight (x1), NaOH% by weight (x2), silicate % by weight (x3), and process temperature (x4)(“Advantages of CEHDP Bleaching for High Brightness Kraft Pulp
Snowpacks contain a wide spectrum of pollutants that may represent environmental hazards. The article “Atmospheric PAH Deposition: Deposition Velocities and Washout Ratios”(J. of Environmental Engineering, 2002: 186–195) focused on the deposition of polyaromatic hydrocarbons. The authors
Utilization of sucrose as a carbon source for the production of chemicals is uneconomical. Beet molasses is a readily available and low-priced substitute. The article “Optimization of the Production of -Carotene from Molasses by Blakeslea Trispora (J. of Chemical Technology and Biotechnology,
The article “The Undrained Strength of Some Thawed Permafrost Soils” (Canadian Geotechnical J., 1979:420–427) contains the following data on undrained shear strength of sandy soil (y, in kPa), depth (x1, in m), and water content (x2, in %).y x1 x2 y y ˆy e ˆ *1 14.7 8.9 31.5 23.35 8.65 1.50
a. When the model Y 0 1x1 2x2 3 x2 1 4 x2 25 x1x2 ! is fit to the hops data of Exercise 49, the estimate of 5 is ˆ5 .557 with estimated standard deviation sˆ5 .94. Test H0: 5 0 versus Ha: 5 0.b. Each t-ratio ˆi/sˆi (i 1, 2, 3, 4, 5) for the model of part(a) is less than 2
The article “The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hops (Agricultural Meteorology, 1974: 375–382) reports the following data on yield (y), mean temperature over the period between date of coming into hops and date of picking (x1), and mean percentage of
In the regression analyses, the three values of each variable were coded as 1, 0, and 1, respectively, giving the accompanying data (the value y8 19.3 was reported, but our value y8 20.3 results in regression output identical to that appearing in the article)?
An experiment to investigate the effects of a new technique for degumming of silk yarn was described in the article “Some Studies in Degumming of Silk with Organic Acids” (J. Society of Dyers and Colourists, 1992: 79–86). One response variable of interest was y weight loss (%). The
Efficient design of certain types of municipal waste incinerators requires that information about energy content of the waste be available. The authors of the article “Modeling the Energy Content of Municipal Solid Waste Using Multiple ?
A regression analysis carried out to relate y repair time for a water filtration system (hr) to x1 elapsed time since the previous service (months) and x2 type of repair (1 if electrical and 0 if mechanical) yielded the following model based on n 12 observations: y .950 .400x1 1.250x2. In
The article “Analysis of the Modeling Methodologies for Predicting the Strength of Air-Jet Spun Yarns” (Textile Res.J., 1997: 39–44) reported on a study carried out to relate yarn tenacity (y, in g/tex) to yarn count (x1, in tex), percentage polyester (x2), first nozzle pressure (x3, in
The authors of the article “An Ultracentrifuge Flour Absorption Method” (Cereal Chemistry, 1978: 96–101)studied the relationship between water absorption for wheat flour and various characteristics of the flour. In particular, the authors used a first-order multiple linear regression model to
An experiment carried out to study the effect of the mole contents of cobalt (x1) and the calcination temperature (x2)on the surface area of an iron–cobalt hydroxide catalyst (y)resulted in the accompanying data (“Structural Changes and Surface Properties of CoxFe3xO4 Spinels,” J. of
An investigation of a die casting process resulted in the accompanying data on x1 furnace temperature, x2 die close time, and y temperature difference on the die surface (“A Multiple-Objective Decision-Making Approach for Assessing Simultaneous Improvement in Die Life and Casting Quality in
The ability of ecologists to identify regions of greatest species richness could have an impact on the preservation of genetic diversity, a major objective of the World Conservation Strategy. The article “Prediction of Rarities from Habitat Variables: Coastal Plain Plants on Nova Scotian
The article “Readability of Liquid Crystal Displays: A Response Surface” (Human Factors, 1983: 185–190) used a multiple regression model with four independent variables to study accuracy in reading liquid crystal displays. The variables were y error percentage for subjects reading a
Let y sales at a fast-food outlet (1000s of $), x1 number of competing outlets within a 1-mile radius, x2 population within a 1-mile radius (1000s of people), and x3 be an indicator variable that equals 1 if the outlet has a drive-up window and 0 otherwise. Suppose that the true regression
Let y wear life of a bearing, x1 oil viscosity, and x2 load. Suppose that the multiple regression model relating life to viscosity and load is Y 125.0 7.75x1 .0950x2 .0090x1x2 !a. What is the mean value of life when viscosity is 40 and load is 1100?b. When viscosity is 30, what is the
A trucking company considered a multiple regression model for relating the dependent variable y total daily travel time for one of its drivers (hours) to the predictors x1 distance traveled (miles) and x2 the number of deliveries made. Suppose that the model equation is Y .800 .060x1 .900x2
Cardiorespiratory fitness is widely recognized as a major component of overall physical well-being. Direct measurement of maximal oxygen uptake (VO2max) is the single best measure of such fitness, but direct measurement is timeconsuming and expensive. It is therefore desirable to have a prediction
The article “The Respiration in Air and in Water of the Limpets Patella caerulea and Patella lusitanica” (Comp.Biochemistry and Physiology, 1975: 407–411) proposed a simple power model for the relationship between respiration rate y and temperature x for P. caerulea in air. However, a plot of
The following data resulted from an experiment to assess the potential of unburnt colliery spoil as a medium for plant growth. The variables are x acid extractable cations and y exchangeable acidity/total cation exchange capacity(“Exchangeable Acidity in Unburnt Colliery Spoil,” Nature,
In many polynomial regression problems, rather than fitting a “centered” regression function using x x x, computational accuracy can be improved by using a function of the standardized independent variable x (x x)/sx, where sx is the standard deviation of the xis. Consider fitting the
The following data is a subset of data obtained in an experiment to study the relationship between soil pH x and y A1.Concentration/EC (“Root Responses of Three Gramineae Species to Soil Acidity in an Oxisol and an Ultisol,” Soil Science, 1973: 295–302):x | 4.01 4.07 4.08 4.10 4.18 y | 1.20
The accompanying data was obtained from a study of a certain method for preparing pure alcohol from refinery streams (“Direct Hydration of Olefins,” Industrial and Eng.Chemistry, 1961: 209–211). The independent variable x is volume hourly space velocity, and the dependent variable y is the
The article “A Simulation-Based Evaluation of Three Cropping Systems on Cracking-Clay Soils in a Summer Rainfall Environment” (Agricultural Meteorology, 1976:211–229) proposes a quadratic model for the relationship between water supply index (x) and farm wheat yield (y).Representative data
High-alumina refractory castables have been extensively investigated in recent years because of their significant advantages over other refractory brick of the same class—lower production and application costs, versatility, and performance at high temperatures. The accompanying data on x
The viscosity (y) of an oil was measured by a cone and plate viscometer at six different cone speeds (x). It was assumed that a quadratic regression model was appropriate, and the estimated regression function resulting from the n 6 observations was y 113.0937 3.3684x .01780x2a. Estimate
The following data on y glucose concentration (g/L) and x fermentation time (days) for a particular blend of malt liquor was read from a scatter plot in the article “Improving Fermentation Productivity with Reverse Osmosis” (Food Tech., 1984: 92–96):x | 12345678 y | 74 54 52 51 52 53 58
In addition to a linear regression of true density on moisture content, the article cited in Exercise 6 considered a quadratic regression of bulk density versus moisture content.Data from a graph in the article follows, along with a MINITAB output from the quadratic fit.The regression equation is
The following data resulted from a study commissioned by a large management consulting company to investigate the relationship between amount of job experience (months) for a junior consultant and the likelihood of the consultant being able to perform a certain complex task.Success 8 13 14 18 20 21

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