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Statistics For Engineers And Scientists 3rd Edition William Navidi - Solutions

A machine that grinds valves is set to produce valves whose lengths have mean 100mmand standard deviation 0.1 mm. The machine is moved to a new location. It is thought that the move may have upset the calibration for the mean length, but that it is unlikely to have changed the standard deviation.
A machine manufactures bolts that are supposed to be 3 inches in length. Each day a quality engineer selects a random sample of 50 bolts from the day's production, measures their lengths, and performs a hypothesis test of H0 :μ = 3 versus H1 :μ = 3, where μ is the mean length of all the bolts
Refer to Exercise 14. The process engineer notices that the sample from line 3 has the lowest proportion of failures. Use the Bonferroni adjustment to determine whether she can conclude that the population proportion of failures on line 3 is less than 0.10. Exercises 16 and 17 illustrate that
The rank-sum test is sometimes thought of as a test for population medians. Under the assumptions of equal spread and shape, the means of two populations will differ if and only if the medians differ; therefore tests for equality of population means are also tests for equality of population
Two different chemical formulations of rocket fuel are considered for the peak thrust they deliver in a particular design for a rocket engine. The thrust/weight ratios (in kilograms force per gram) for each of the two fuels are measured several times. The results are as follows:a. Assume the fuel
The article "Valuing Watershed Quality Improvements Using Conjoint Analysis" (S. Farber and B. Griner, Ecological Economics, 2000:63-76) presents the results of a mail survey designed to assess opinions on the value of improvement efforts in an acid-mine degraded watershed in Western Pennsylvania.
A new quality-inspection program is being tested to see if it will reduce the proportion of parts shipped out that are defective. Under the old program, the proportion of defective parts was 0.10. Two hundred parts that passed inspection under the new program will be sampled, and the number of
Suppose you have purchased a filling machine for candy bags that is supposed to fill each bag with 16 oz of candy. Assume that the weights of filled bags are approximately normally distributed. A random sample of 10 bags yields the following data (in oz):On the basis of these data, can you conclude
An automobile manufacturer wishes to compare the lifetimes of two brands of tire. She obtains samples of six tires of each brand. On each of six cars, she mounts one tire of each brand on each front wheel. The cars are driven until only 20% of the original tread remains. The distances, in miles,
There is concern that increased industrialization may be increasing the mineral content of river water. Ten years ago, the silicon content of the water in a certain river was 5 mg/L. Eighty-five water samples taken recently from the river have mean silicon content 5.6 mg/L and standard deviation
Compute the correlation coefficient for the following data set.
The article "Drift in Posturography Systems EquippedWith a Piezoelectric Force Platform: Analysis and Numerical Compensation" (L. Quagliarella, N. Sasanelli, and V. Monaco, IEEE Transactions on Instrumentation and Measurement, 2008: 997-1004), reported the results of an experiment to determine the
The article "'Little Ice Age' Proxy Glacier Mall Balance Records Reconstructed from Tree Rings in the Mt. Waddington Area, British Columbia Coast Mountains, Canada" (S Larocque and D. Smith, The Holocene, 2005:748-757) evaluates the use of tree ring widths to estimate changes in the masses of
For each of the following scatterplots, state whether the correlation coefficient is an appropriate summary, and explain briefly.(a)(b) (c)
An investigator collected data on heights and weights of college students. The correlation between height and weight for men was about 0.6, and for women it was about the same. If men and women are taken together, will the correlation between height and weight be more than 0.6, less than 0.6, or
A chemical engineer is studying the effect of temperature and stirring rate on the yield of a certain product. The process is run 16 times, at the settings indicated in the following table. The units for yield are percent of a theoretical maximum.a. Compute the correlation between temperature and
Tire pressure (in kPa) was measured for the right and left front tires on a sample of 10 automobiles. Assume that the tire pressures follow a bivariate normal distribution. Right Tire Left Tire Pressure
Each month for several months, the average temperature in ◦C (x) and the number of pounds of steam (y) consumed by a certain chemical plant were measured. The least-squares line computed from the resulting data is y = 245.82 + 1.13x. a. Predict the number of pounds of steam consumed in a month
An agricultural scientist planted alfalfa on several plots of land, identical except for the soil pH. Following are the dry matter yields (in pounds per acre) for each plot. pH
Varying amounts of pectin were added to canned jellies, to study the relationship between pectin concentration in % (x) and a firmness index (y). The means and standard deviations of the x and y values were = 3, sx = 0.5, = 50, sy = 10. The correlation between curing time and firmness was
A simple random sample of 100 men aged 25-34 averaged 70 inches in height, and had a standard deviation of 3 inches. Their incomes averaged $34,900 and had a standard deviation of $17,200. Fill in the blank: From the least-squares line, we would predict that the income of a man 70 inches tall would
In Galton's height data (Figure 7.1, in Section 7.1), the least-squares line for predicting forearm length (y) from height (x) is y = −0.2967 + 0.2738x. a. Predict the forearm length of a man whose height is 70 in. b. How tall must a man be so that we would predict his forearm length to be 19
Moisture content in percent by volume (x) and conductivity in mS/m (y) were measured for 50 soil specimens. The means and standard deviations were = 8.1, sx = 1.2, = 30.4, sy = 1.9. The correlation between conductivity and moisturewas computed to be r = 0.85. Find the equation of the
The article "Testing the Influence of Climate, Human Impact and Fire on the Holocene Population Expansion of Fagus sylvatica in the Southern Prealps (Italy)" (V. Valsecchi, W. Flnsinger, et al., The Holocene 2008:603-614) presents calculations of the ages (in calendar years before 1950) of several
A chemical reaction is run 12 times, and the temperature xi (in —¦C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded:Let Î²0 represent the hypothetical yield at a temperature of 0—¦C, and
In the weld data (Example 7.17) imagine that 95% confidence intervals are computed for the mean strength of welds with oxygen contents of 1.3, 1.5, and 1.8 parts per thousand. Which of the confidence intervals would be the shortest? Which would be the longest?
In the following MINITAB output, some of the numbers have been accidentally erased. Recompute them, using the numbers still available. There are n = 25 points in the data set.
In order to increase the production of gas wells, a procedure known as "fracture treatment" is often used. Fracture fluid, which consists of fluid mixed with sand, is pumped into the well. The following figure presents a scatterplot of the monthly production versus the volume of fracture fluid
Ozone (O3) is a major component of air pollution in many cities. Atmospheric ozone levels are influenced by many factors, including weather. In one study, the mean percent relative humidity (x) and the mean ozone levels (y) were measured for 120 days in a western city. Mean ozone levels were
Refer to Exercises 3 and 4. An atmospheric scientist notices that the slope of the least-squares line in the study described in Exercise 4 differs from the one in the study described in Exercise 3. He wishes to test the hypothesis that the effect of humidity on ozone level differs between the two
The coefficient of absorption (COA) for a clay brick is the ratio of the amount of cold water to the amount of boiling water that the brick will absorb. The article "Effects of Waste Glass Additions on the Properties and Durability of Fired Clay Brick" (S. Chidiac and L. Federico, Can J Civ Eng,
In a study to determine the relationship between ambient outdoor temperature and the rate of evaporation of water from soil, measurements of average daytime temperature in —¦C and evaporation in mm/day were taken for 40 days. The results are shown in the following table.a. Compute the
The following output (from MINITAB) is for the least-squares fit of the model ln y = Î²0 + Î²1 ln x + Îµ, where y represents the monthly production of a gas well and x represents the volume of fracture fluid pumped in. (A scatterplot of these data is presented in
The article "The Equilibrium Partitioning of Titanium Between Ti3+ and Ti4+ Valency States in CaO-SiO2-TiOx Slags" (G. Tranell, O. Ostrovski, and S. Jahanshahi, Metallurgical and Materials Transactions B, 2002:61-66) discusses the relationship between the redox ratio Ti3+/Ti4+ and oxygen partial
The article "Some Parameters of the Population Biology of Spotted Flounder (Ciutharus linguatula Linnaeus, 1758) in Edremit Bay (North Aegean Sea)" (D. T¨urker, B. Bayhan, et al., Turkish Journal of Veterinary and Animal Science, 2005:1013-1018) models the relationship between weight W and length
To determine the effect of temperature on the yield of a certain chemical process, the process is run 24 times at various temperatures. The temperature (in —¦C) and the yield (expressed as a percentage of a theoretical maximum) for each run are given in the following table. The results
Good forecasting and control of preconstruction activities leads to more efficient use of time and resources in highway construction projects. Data on construction costs (in $1000s) and person-hours of labor required on several projects are presented in the following table and are taken from the
The National Assessment for Educational Progress measured the percentage of eighth grade students who were proficient in reading and the percentage of students who graduated from high school in each state in the U.S. The results for the ten most populous states are as follows:a. Construct a
A windmill is used to generate direct current. Data are collected on 45 different days to determine the relationship between wind speed in mi/h (x) and current in kA (y). The data are presented in the following table.a. Compute the least-squares line for predicting y from x. Make a plot of
The Beer-Lambert law relates the absorbance A of a solution to the concentration C of a species in solution by A = MLC, where L is the path length and M is the molar absorption coefficient. Assume that L = 1 cm. Measurements of A are made at various concentrations. The data are presented in the
The article "Estimating Population Abundance in Plant Species with Dormant Life-Stages: Fire and the Endangered Plant Grevillea caleye R. Br." (T. Auld and J. Scott, Ecological Management and Restoration, 2004:125-129) presents estimates of population sizes of a certain rare shrub in areas burnt by
Monitoring the yield of a particular chemical reaction at various reaction vessel temperatures produces the results shown in the following table.a. Find the least-squares estimates for Î²0, Î²1, and Ïƒ2 for the simple linear model Yield = Î²0 +
The article "Low-Temperature Heat Capacity and Thermodynamic Properties of 1,1,1-trifluoro-2,2-dichloroethane" (R. Varushchenko and A. Druzhinina, Fluid Phase Equilibria, 2002:109-119) describes an experiment in which samples of Freon R-123 were melted in a calorimeter. Various quantities of energy
Consider the model y = βx + ε, where the intercept of the line is known to be zero. Assume that values (x1, y1) , . . . , (xn, yn) are observed, and the least-squares estimate β of β is to be computed. a. Derive the least-squares estimate β in terms of xi and yi. b. Let σ2 denote the variance
Use Equation (7.35) (page 541) to show that Î¼Î²0 = Î²0.
Use Equation (7.35) (page 541) to derive the formulaEquation (7.35)
Eruptions of the Old Faithful geyser in Yellowstone National Park typically last from 1.5 to 5 minutes. Between eruptions are dormant periods, which typically last from 50 to 100 minutes. A dormant period can also be thought of as the waiting time between eruptions. The durations in minutes for 60
A chemist is calibrating a spectrophotometer that will be used to measure the concentration of carbon monoxide (CO) in atmospheric samples. To check the calibration, samples of known concentration are measured. The true concentrations (x) and the measured concentrations (y) are given in the
The article "A Robust Optimization Approach for the Capacitated Vehicle Routing Problem With Demand Uncertainty" (I. Sungur, F. Ordonez, and M. Dessouky, IIE Transactions, 2008:509-523) discusses methods to reduce transportation costs while satisfying demands. In one study, the percent demand that
The article "Copper Oxide Mounted on Activated Carbon as Catalyst for Wet Air Oxidation of Aqueous Phenol. 1. Kinetic and Mechanistic Approaches" (P. Alvarez, D. McLurgh, and P. Plucinski, Industrial Engineering and Chemistry Research, 2002: 2147-2152) reports the results of experiments to describe
In an experiment to determine the factors affecting tensile strength in steel plates, the tensile strength (in kg/mm2), the manganese content (in parts per thousand), and the thickness (in mm) were measured for a sample of 20 plates. The following MINITAB output presents the results of fitting the
The following MINITAB output is for a multiple regression. Something went wrong with the printer, so some of the numbers are missing. Fill in the missing numbers.
The article "Evaluating Vent Manifold Inerting Requirements: Flash Point Modeling for Organic Acid-Water Mixtures" (R. Garland and M. Malcolm, Process Safety Progress, 2002:254-260) presents a model to predict the flash point (in —¦F) of a mixture of water, acetic acid, propionic acid,
The following data were collected in an experiment to study the relationship between extrusion pressure (in KPa) and wear (in mg).The least-squares quadratic model is y = ˆ’32.445714 + 0.43154286x ˆ’ 0.000982857x2. a. Using this equation, compute the residuals. b. Compute the
The November 24, 2001, issue of The Economist published economic data for 15 industrialized nations. Included were the percent changes in gross domestic product (GDP), industrial production (IP), consumer prices (CP), and producer prices (PP) from Fall 2000 to Fall 2001, and the unemployment rate
In an experiment to estimate the acceleration of an object down an inclined plane, the object is released and its distance in meters (y) from the top of the plane is measured every 0.1 second from time t = 0.1 to t = 1.0. The data are presented in the following table. t
The data used to fit the model in Exercise 1 are presented in the following table, along with the residuals and the fitted values. Plot the residuals versus the fitted values. Does the plot indicate that the linear model is reasonable? Explain.
In the article "Application of Statistical Design in the Leaching Study of Low-Grade Manganese Ore Using Aqueous Sulfur Dioxide" (P. Naik, L. Sukla, and S. Das, Separation Science and Technology, 2002:1375-1389), a fitted model for predicting the extraction of manganese in % (y) from particle size
In a study of the lung function of children, the volume of air exhaled under force in one second is called FEV1. (FEV1 stands for forced expiratory volume in one second.) Measurements were made on a group of children each year for two years. A linear model was fit to predict this year's FEV1 as a
The article "Drying of Pulps in Sprouted Bed: Effect of Composition on Dryer Performance" (M. Medeiros, S. Rocha, et al., Drying Technology, 2002:865-881) presents measurements of pH, viscosity (in kg/m · s), density (in g/cm3), and BRIX (in percent). The following MINITAB output presents
In an experiment to determine factors related to weld toughness, the Charpy V-notch impact toughness in ft · lb (y) was measured for 22 welds at 0—¦C, along with the lateral expansion at the notch in % (x1), and the brittle fracture surface in % (x2). The data are presented in
Two chemical engineers, A and B, are working independently to develop a model to predict the viscosity of a product (y) from the pH (x1) and the concentration of a certain catalyst (x2). Each engineer has fit the linear modely = Î²0 + Î²1x1 + Î²2x2 +
Refer to Exercise 10 in Section 7.4. a. Divide the data into two groups: points where R1 < 4 in one group, points where R1 ≥ 4 in the other. Compute the least-squares line for predicting R2 from R1 for each group. (You already did this if you did Exercise 10c in Section 7.4.) b. For one of the
True or false: a. For any set of data, there is always one best model. b. When there is no physical theory to specify a model, there is usually no best model, but many that are about equally good. c. Model selection methods such as best subsets and stepwise regression, when properly used, are
In a study of the causes of bearing wear, a machine was run 24 times, with various loads (denoted x1), oil viscosities (x2), and ambient temperatures (x3). The wear, denoted y, was modeled as y = β0 + β1x1 + β2x2 + β3x3 + β4x1x2 + β5x1x3 + β6x2x3 + ε. When this model was fit to the data,
The article "Ultimate Load Analysis of Plate Reinforced Concrete Beams" (N. Subedi and P. Baglin, Engineering Structures, 2001:1068-1079) presents theoretical and measured ultimate strengths (in kN) for a sample of steelreinforced concrete beams. The results are presented in the following table
The article "Vehicle-Arrival Characteristics at Urban Uncontrolled Intersections" (V. Rengaraju and V. Rao, Journal of Transportation Engineering, 1995:317-323) presents data on traffic characteristics at 10 intersections in Madras, India. The following table provides data on road width in m (x1),
The article "Modeling Resilient Modulus and Temperature Correction for Saudi Roads" (H. Wahhab, I. Asi, and R. Ramadhan, Journal of Materials in Civil Engineering, 2001:298-305) describes a study designed to predict the resilient modulus of pavement from physical properties. The following table
To try to improve the prediction of FEV1, additional independent variables are included in the model. These new variables are Weight (in kg), the product (interaction) of Height and Weight, and the ambient temperature (in —¦C). The following MINITAB output presents results of fitting
The article "Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds" (D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s-136s) reports an experiment to predict various properties of titanium welds. Among other properties, the elongation (in
The data presented in the following table give the tensile strength in psi (y) of paper as a function of the percentage of hardwood content (x).a. Fit polynomial models of degrees 1, 2, and so on to predict tensile strength from hardwood content. For each one, use the F test to compare it with the
A paint company collects data on the durability of its paint and that of its competitors. They measured the lifetimes of three samples of each type of paint in several American cities. The results are given in Table SE13.TABLE SE13a. Prior testing suggests that the most important factors that
The article "Measurements of the Thermal Conductivity and Thermal Diffusivity of Polymer Melts with the Short- Hot-Wire Method" (X. Zhang, W. Hendro, et al., International Journal of Thermophysics, 2002:1077-1090) reports measurements of the thermal conductivity (inW·mˆ’1 ·
The article "Groundwater Electromagnetic Imaging in Complex Geological and Topographical Regions: A Case Study of a Tectonic Boundary in the French Alps" (S. Houtot, P. Tarits, et al., Geophysics, 2002:1048-1060) presents measurements of concentrations of several chemicals (in mmol/L) and
The article "Lead Dissolution from Lead Smelter Slags Using Magnesium Chloride Solutions" (A. Xenidis, T. Lillis, and I. Hallikia, The AusIMM Proceedings, 1999:37-44) discusses an investigation of leaching rates of lead in solutions of magnesium chloride. The data in the following table (read from
The article "Estimating Resource Requirements at Conceptual Design Stage Using Neural Networks" (A. Elazouni, I. Nosair, et al., Journal of Computing in Civil Engineering, 1997:217-223) suggests that certain resource requirements in the construction of concrete silos can be predicted from a model.
The following MINITAB output is for a multiple regression. Some of the numbers got smudged, becoming illegible. Fill in the missing numbers.
In a simulation of 30 mobile computer networks, the average speed, pause time, and number of neighbors were measured. A "neighbor" is a computer within the transmission range of another. The data are presented in the following table.a. Fit the model with Neighbors as the dependent variable, and
In a study to predict temperature from air pressure in a piston-cylinder device, 19 measurements were made of temperature in —¦f (y) and air pressure in psi (x). three models were fit: the linear model y = Î²0 + Î²1x + Îµ, the quadratic model y =
Refer to Exercise 2 in Section 8.2. a. Using each of the three models in turn, predict the NOx emission when Speed = 1500, Torque = 400, and HP = 150. b. Using each of the three models in turn, predict the NOx emission when Speed = 1600, Torque = 300, and HP = 100. c. Using each of the three models
A study is made of the effect of curing temperature on the compressive strength of a certain type of concrete. Five concrete specimens are cured at each of four temperatures, and the compressive strength of each specimen is measured (in MPa). The results are as follows:a. Construct an ANOVA table.
An experiment was performed to determine whether the annealing temperature of ductile iron affects its tensile strength. Five specimens were annealed at each of four temperatures. The tensile strength (in ksi) was measured for each. The results are presented in the following table.a. Construct an
Refer to Exercise 13. a. Compute the quantity s =√MSE, the estimate of the error standard deviation σ. b. Assuming s to be the error standard deviation, find the sample size necessary in each treatment to provide a power of 0.90 to detect a maximum difference of 2 in the treatment means at the
The article "Multi-objective Scheduling Problems: Determination of Pruned Pareto Sets" (H. Taboada and D. Coit, IIE Transactions, 2008:552-564), presents examples in a discussion of optimization methods for industrial scheduling and production planning. In one example, seven different jobs were
The article "Solid-Phase Chemical Fractionation of Selected Trace Metals in Some Northern Kentucky Soils" (A. Karathanasis and J. Pils, Soil and Sediment Contamination, 2005:293-308) presents pH measurements of soil specimens taken from three different types of soils. The results in the following
The removal of ammoniacal nitrogen is an important aspect of treatment of leachate at landfill sites. The rate of removal (in percent per day) is recorded for several days for each of several treatment methods. The results are presented in the following table. (Based on the article "Removal of
The article "Influence of Age on Masonry Bond Strength and Mortar Microstructure" (H. Sugo, A. Page, and S. Lawrence, Can J Civ Eng, 2007:1433-1442) investigates the effect of age on tensile strength of mortar. Several specimens of various ages were loaded until failure, and the maximum load (in
The article "Secretion of Parathyroid Hormone Oscillates Depending on the Change in Serum Ionized Calcium During Hemodialysis and May Affect Bone Metabolism" (T. Kitahara, K, Ueki et al., Nephron Clinical Practice, 2005:c9-c17) presents measurements of basal ionized calcium (Ca) levels for four
A certain chemical reaction was run three times at each of three temperatures. The yields, expressed as a percent of a theoretical maximum, were as follows:a. Construct an ANOVA table. You may give a range for the P-value. b. Can you conclude that the mean yield differs with temperature?
The article "Organic Recycling for Soil Quality Conservation in a Sub-Tropical Plateau Region" (K. Chakrabarti, B. Sarkar, et al., J. Agronomy and Crop Science, 2000:137-142) reports an experiment in which soil specimens were treated with six different treatments, with two replicates per treatment,
Refer to Exercise 16 in Section 9.1. a. Use the Fisher LSD method to find a 95% confidence interval for the difference between the means for a diameter of 16 and a diameter of 36. b. Use the Tukey-Kramer method to determine which pairs of diameters, if any, differ at the 5% level.
In an experiment to determine the effect of catalyst on the yield of a certain reaction, the mean yields for reactions run with each of four catalysts were X̅1. = 89.88, X̅2. = 89.51, X̅3. = 86.98, and X̅4. = 85.79. Assume that five runs were made with each catalyst. a. If MSE = 3.85, compute
For some data sets, the F statistic will reject the null hypothesis of no difference in mean yields, but the Tukey-Kramer method will not find any pair of means that can be concluded to differ. For the four sample means given in Exercise 13, assuming a sample size of 5 for each treatment, find a
Acrylic resins used in the fabrication of dentures should not absorb much water, since water sorption reduces strength. The article "Reinforcement of Acrylic Resin for Provisional Fixed Restorations. Part III: Effects of Addition of Titania and Zirconia Mixtures on Some Mechanical and Physical
Refer to Exercise 13 in Section 9.1. a. Use the Bonferroni method to determine which pairs of means, if any, are different at the 5% level. b. Use the Tukey-Kramer method to determine which pairs of means, if any, are different at the 5% level. c. Which is the more powerful method to find all the
Refer to Exercise 13 in Section 9.1.Ametallurgistwants to determine whether the mean tensile strength for specimens annealed at 900◦C differs from the mean strengths for specimens annealed at 750◦C, 800◦C, and 850◦C. a. Use the Bonferroni method to determine which of the means, if any, for
Refer to Exercise 5 in Section 9.1. a. Use the Fisher LSD method to find a 95% confidence interval for the difference between the means for specimens aged 3 days and specimens aged 365 days. b. Use the Tukey-Kramer method to determine which pairs of treatments, if any, differ at the 5% level.
To assess the effect of piston ring type and oil type on piston ring wear, three types of piston ring and four types of oil were studied. Three replications of an experiment, in which the number of milligrams of material lost from the ring in four hours of running was measured, were carried out for
Artificial joints consist of a ceramic ball mounted on a taper. The article "Friction in Orthopaedic Zirconia Taper Assemblies" (W. Macdonald, A. Aspenberg, et al., Proceedings of the Institution of Mechanical Engineers, 2000: 685-692) presents data on the coefficient of friction for a push-on load
Refer to Exercise 12. The treatments with a delivery ratio of 1:0 were controls, or blanks. It was discovered after the experiment that the high apparent levels of sorption in these controls was largely due to volatility of the trifluralin. Eliminate the control treatments from the data. a.

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