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engineering
statistics for engineering and the sciences
Statistics For Engineering And The Sciences 6th Edition William M. Mendenhall, Terry L. Sincich - Solutions
The Journal of Human Stress (Summer 1987) reported on a study of “psychological response of firefighters to a chemical fire.” The researchers used multiple regression to predict emotional distress as a function of the following independent variables. Identify each independent variable as
Refer to the Environmental Science & Technology study of sorption of organic vapors, Exercise 12.7. Consider modeling the vapor retention coefficient y as a function of one of the two quantitative variables, temperature (x1) and relative humidity (x2).a. Propose a model that hypothesizes a
The Journal of Space Engineering (Vol. 4, 2011) investigated the properties of large, deployable space membranes used to store structures such as solar sails, antennas, sunshields, and solar power satellites. These membranes are susceptible to creases during folding and packaging, which can have a
A study of the atmospheric pollution on the slopes of the Blue Ridge Mountains (Tennessee) was conducted. The file LEADMOSS contains the levels of lead found in 70 fern moss specimens (in micrograms of lead per gram of moss tissue) collected from the mountain slopes, as well as the elevation of the
Refer to the Human Factors study of the performance of a computerized speech recognizer, Exercise 12.26. Recall that the researchers built a complete second-order model for task completion time (y) as a function of accuracy (x1) and vocabulary (x2).a. Give the null hypothesis for testing whether
An experiment was conducted to evaluate the performances of a diesel engine run on synthetic (coal-derived) and petroleum-derived fuel oil (Journal of Energy Resources Technology, Mar. 1990). The petroleum-derived fuel used was a number 2 diesel fuel (DF-2) obtained from Phillips Chemical Company.
Many cognitively demanding jobs (e.g., air traffic controller, radar/sonar operator) require efficient processing of visual information. Researchers at Georgia Tech investigated the variables that affect the reaction time of subjects performing a visual search task (Human Factors, June 1993).
Oil wells can suffer from scale deposits, leading to a reduction in well flow performance. Consequently, it is important for oil well managers to periodically assess the damage caused by scale deposits. In the Journal of Petroleum & Gas Engineering (April 2013) researchers compared four
A trade-off study regarding the inspection and test of transformer parts was conducted by the quality department of a major defense contractor. The investigation was structured to examine the effects of varying inspection levels and incoming test times to detect early part failure or fatigue. The
In increasingly severe oil well environments, oil producers are interested in high-strength nickel alloys that are corrosion-resistant. Since nickel alloys are especially susceptible to hydrogen embrittlement, an experiment was conducted to compare the yield strengths of nickel alloy tensile
Refer to Exercise 14.8. Use Bonferroni’s method to compare the mean heat rates of the three gas turbine engines. Use α = .06.Data from Exercise 14.8Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of gas turbines augmented with high-pressure inlet fogging,
Refer to Exercise 14.11. Use a multiple comparisons procedure to compare the mean Al/Be ratios for the five boreholes. Identify the means that appear to differ. Use α = .05.Data from Exercise 14.11Refer to the American Journal of Science (Jan. 2005) study of the chemical makeup of buried tills
Refer to the Behavioral Neuroscience (Feb. 2004) study of the drug scopolamine’s effects on memory for word-pair associates, Exercise 14.13. Recall that the researchers theorized that the mean number of word pairs recalled for the scopolamine subjects (group 1) would be less than the
Refer to Exercise 14.19. Use a multiple comparisons procedure to compare the mean crack widths for the four wetting periods. Identify the means that appear to differ. Use α = .05.Data from Exercise 14.19The Perth (Australia) Metropolitan Water Authority recently completed construction of a land
In Ecological Engineering (Feb. 2004), a new methodology for tree seedling production (called aqua-forest system) was compared to a conventional tree nursery method. The new method was applied to four plants grown in a clean-water creek (Treatment T1) and four plants grown in a polluted water creek
Construct an R-chart for the data of Exercise 16.15. Does the process variation appear to be in control?Data from Exercise 16.15Refer to the manufacture of a rheostat knob, Exercise 16.7. To monitor the process mean, five knobs from each hour’s production were randomly sampled and the distance
A quality control inspector is studying the alternative sampling plans (n = 5, a = 1) and (n = 25, a = 5).a. Sketch the operating characteristic curves for both plans, using lot fractions defective .05, .10, .20, .30, and .40.b. As a seller producing lots with AQL = .10, which of the two sampling
An experiment was conducted to investigate the sheet flow rate of a land waste treatment plant. Classify each of the following independent variables as quantitative or qualitative and describe the levels the variables might assume.a. Amount of rainfallb. Method of treatmentc. Irrigation rated.
Environmental Science & Technology (Oct. 1993) published an article that investigated the variables that affect the sorption of organic vapors on clay minerals. The independent variables and levels considered in the study are listed here. Identify the type (quantitative or qualitative) of
The accompanying graphs depict pth-order polynomials for one quantitative independent variable.a. For each graph, identify the order of the polynomial. b. Using the parameters β0, β1, β2, etc., write an appropriate model relating E(y) to x for each graph.c. The signs (+ or -) of many of the
Graph the following polynomials and identify the order of each on your graph:a. E(y) = 2 + 3xb. E(y) = 2 + 3x2c. E(y) = 1 + 2x + 2x2 + x3d. E(y) = 2x + 2x2 + x3e. E(y) = 2 - 3x2f. E(y) = -2 + 3x
The amount of pressure used to produce a certain plastic is thought to be related to the strength of the plastic. Researchers believe that, as pressure is increased, the strength of the plastic increases until, at some point, increases in pressure will have a detrimental effect on strength. Write a
The lane utilization of a highway is measured by how the traffic flow in one direction is distributed among the available lanes. A lane utilization model for highways in the United Kingdom was developed in the Journal of Transportation Engineering (May 2013). The dependent variable in the analysis
The level of overcrowding for passengers waiting at a train station was investigated in the Journal of Transportation Engineering (June 2013). The researchers measured “crowdedness” as the average distance between the forefront edge of the passenger waiting on a platform and the rear edge of
Does exercise improve the human immune system? An experiment was conducted by a physiologist at the University of Florida to determine whether such a relationship exists. Thirty subjects volunteered to participate in the study. The amount of immunoglobulin known as IgG (an indicator of long-term
The National Snow and Ice Data Center at the University of New Hampshire collected data on the temperature of ice core samples from a glacier snow pit. The ice core samples were collected from depths ranging from 2 meters to 175.5 meters. The data for depths up to 20 meters are listed in the next
Suppose the true relationship between E(y) and the quantitative independent variables x1 and x2 is described by the following first-order model:E(y) = 4 - x1 + 2x2a. Describe the corresponding response surface.b. Plot the contour lines of the response surface for x1 = 2, 3, 4,where 0 ≤ x2 ≤
Suppose the true relationship between E(y) and the quantitative independent variables x1 and x2 is E(y) = 4 - x1 + 2x2 + x1x2 Answer the questions posed in Exercise 12.16. Explain the effect of the interaction term on the mean response E(y).
Refer to the Environmental Science & Technology study of sorption of organic vapors, Exercise 12.7. Consider modeling the retention coefficient y as a function of bothx1 = Temperature (degrees)x2 = Relative humidity (percent)a. Write a first-order model for E(y).b. Write a complete second-order
A Harvard University biologist used multiple regression to model the swimming speed of an American eel. (Proceedings of the Royal Society, B, Dec. 2004.) Steady swimming speed, y (body lengths per second), was modeled as a function of the quantitative variables body wave speed, x1 (body lengths per
Refer to the Journal of Transportation Engineering (May 2013) study of the lane utilization of a highway, Exercise 12.13. Recall that the dependent variable in the analysis was lane utilization y, measured as the percentage of vehicles in the lane. The researchers used two independent variables
Research in the International Journal of Foresting Engineering (Vol. 19, 2008) investigated the muscle activity patterns in the neck and upper extremities exhibited during a work day among forestry vehicle operators. For one portion of the study, the researchers compared the muscle activity of
Data on the polysilicon thickness of semiconductor wafers processed using rapid thermal chemical vapor deposition was analyzed in the Journal of the American Statistical Association (March 1998). The polysilicon thickness measurements (in angstroms) as well as the thickness of oxide applied to the
An exploration seismologist wants to develop a model that will allow him to estimate the average signal-to-noise ratio of an earthquake’s seismic wave, y, as a function of two independent variables: x1 = Frequency (cycles per second)x2 = Amplitude of the waveleta. Identify the independent
A study reported in Human Factors (Apr. 1990) investigated the effects of recognizer accuracy and vocabulary size on the performance of a computerized speech recognition device. Accuracy (x1) of the device, measured as the percentage of correctly recognized spoken utterances, was set at three
Refer to the Engineering Project Organizational Journal (Vol. 3., 2013) study of how the emotional intelligence of individual team members relates directly to the performance of their team, Exercise 11.23. Recall that students enrolled in the course, Introduction to the Building Industry, completed
Refer to the Engineering Structures and Technologies (Sep. 2012) study on the use of processed straw as thermal insulation for homes, Exercise 11.4. You used data on n = 25 straw specimens (see right column) to fit a quadratic model relating y = thermal conductivity (watts per meter- Kelvin) and x
Suppose you want to use the coding system for observational data to fit a second-order model to the tire pressure–automobile mileage data given in the next table below.a. Give the equation relating the coded variable u to pressure, x, using the coding system for observational data.b. Calculate
Refer to the Journal of Transportation Engineering (June 2013) study of overcrowding at a train station, Exercise 12.14. Using data collected for a sample of 20 train stops (see below), you analyzed the quadratic model, E(y) = β0 + β1x1 + β2x2, where y = average distance (meters) between
Refer to the IHS Journal of Hydraulic Engineering (September 2012) study of the repair and replacement of water pipes, Exercise 11.37. Recall that a team of civil engineers used regression analysis to model y = the ratio of repair to replacement cost of commercial pipe as a function of x = the
Refer to the Journal of Agricultural, Biological, and Environmental Statistics (March 2005) study of the chemical composition of rainwater, Exercise 12.1. Recall that the nitrate concentration, y (milligrams per liter), in a rainwater sample was modeled as a function of water source (groundwater,
Refer to the Journal of Human Stress study of firefighters, Exercise 12.5. Consider using the qualitative variable, level of social support, as a predictor of emotional stress y. Suppose that four social support levels were studied: none, low, moderate, and high.a. Write a model for E(y) as a
Refer to the Environmental Science & Technology study of sorption of organic vapors, Exercise 12.7. Consider using the qualitative variable, organic compound, as a predictor of the retention coefficient y. Recall that five organic compounds were studied: benzene, toluene, chloroform, methanol,
Refer to the International Journal of Foresting Engineering (Vol. 19, 2008) study of neck muscle activity patterns among forestry vehicle operators, Exercise 12.23. Recall that the researchers identified the key explanatory variables of y = the number of sustained low-level muscle activity (SULMA)
An electrical engineer wants to compare the mean life lengths (in hours) of five different brands of magnetron tubes. Data are gathered on 10 magnetron tubes selected at random from each of the five brands. Write a model that will give the mean life length for the five brands and interpret
Because of the hot, humid weather conditions in Florida, the growth rates of beef cattle and the milk production of dairy cows typically decline during the summer. However, agricultural and environmental engineers have found that a well-designed shade structure can significantly increase the milk
Evolutionary Ecology Research (July 2003) published a study of the patterns of extinction in the New Zealand bird population. The NZBIRDS file contains qualitative data on flight capability (volant or flightless), habitat (aquatic, ground terrestrial, or aerial terrestrial), nesting site (ground,
Wastewater treatment systems are designed to maintain the chemical, physical, and biological integrity of water. These systems, however, tend to generate various greenhouse gases, such as methane (CH4). The Journal of the Institute of Engineering (Vol. 8, 2011) published a study of the amount of
Corporate sustainability refers to business practices designed around social and environmental considerations (e.g., “going green” and energy conservation). Business and Society (March 2011) published a paper on how firm size and firm type impacts sustainability behaviors. Nearly 1,000 senior
Refer to the Environmental Science & Technology study of sorption of organic vapors, Exercise 12.7. The independent variables used to model the retention coefficient y arex1 = Temperature (degrees)x2 = Relative humidity (percent)Organic compound = (benzene, toluene, chloroform, methanol, and
Refer to the International Journal of Foresting Engineering (Vol. 19, 2008) study of neck muscle activity patterns among forestry vehicle operators, Exercises 12.23 and 12.36. Recall that the researchers identified the key explanatory variables of y = the number of sustained low-level muscle
Eli Lilly and Company has developed three methods (G, R1, and R2) for estimating the shelf life of its drug products based on the potency of the drug.* One way to compare the three methods is to build a regression model for the dependent variable, estimated shelf life y (as a percent of true shelf
An experiment was conducted to compare four Web browsers on their ability to display graphics. (Journal of Graphic Engineering Design, Vol. 3, 2012.) The four browsers were the latest versions of Google Chrome, Mozilla Firefox, Opera and Apple Safari. Each browser was tested on its ability to
Refer to the Journal of the Institute of Engineering (Vol. 8, 2011) study of methane gas (milligrams per liter) emitted from wastewater treatment sludge, Exercise 12.42. Recall that two different types of treated sludge were investigated: (1) sludge without nutrients added and (2) sludge with
Refer to the International Journal of Foresting Engineering (Vol. 19, 2008) study of neck muscle activity patterns among forestry vehicle operators, Exercise 12.23. Recall that the researchers identified the key explanatory variables of y = the number of sustained low-level muscle activity (SULMA)
Refer to the Journal of the Institute of Engineering (Vol. 8, 2011) study of methane gas (milligrams per liter) emitted from wastewater treatment sludge, Exercises 12.42 and 12.51. Recall that two different types of treated sludge were investigated: (1) sludge without nutrients added and (2) sludge
The American Educational Research Journal (Fall 1998) published a study of students’ perceptions of their science ability in hands-on classrooms. A first-order, main effects model that was used to predict ability perception (y) included the following independent variables:Control Variablesx1 =
Refer to the Journal of Colloid and Interface Science study of water/oil mixtures, Exercise 11.27. Recall that three of the seven variables used to predict voltage (y) were volume (x1), salinity (x2), and surfactant concentration (x5). The model the researchers fit isE(y) = β0 + β1x1 + β2x2 +
Refer to Exercise 12.25, in which an exploration seismologist wants to develop a regression model for estimating the mean signal-to-noise ratio of seismic waves from earthquakes. The model under consideration is a complete second-order model:E(y) = β0 + β1x1 + β2x2 + β3x1x2 + + β4x12 +
Refer to the Journal of Human Stress study of firefighters, Exercise 12.5. It is thought that a complete second-order model, shown here, will be adequate to describe the relationship between emotional distress and years of experience for two groups of firefighters—those exposed to a chemical fire
Refer to the Environmental Science & Technology study of sorption of organic vapors, Exercise 12.45. Consider using the quantitative variable, relative humidity, and the qualitative variable, organic compound (at five levels), to model the retention coefficient y.a. Write a complete
A building materials engineer is experimenting with three different cement mixes—dry, damp, and wet—for laying concrete. Since the compressive strength of a concrete slab varies as a function of hardening time and cement mix, the following main effects model is proposed:E(y) = β0 + β1x1 +
An operations manager is interested in modeling E(y), the expected length of time per month (in hours) that a machine will be shut down for repairs, as a function of the type of machine (001 or 002) and the age of the machine (in years).a. Write a complete second-order model for machine downtime
There are six independent variables, x1, x2, x3, x4, x5, and x6, that might be useful in predicting a response y. A total of n = 50 observations are available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to be useful.a. How many models
Fossilized human footprints provide a direct source of information on the gait dynamics of extinct species. How paleontologists and anthropologists interpret these prints, however, may vary. To gain insight into this phenomenon, a group of scientists used human subjects (16 young adults) to
A marine biologist was hired by the EPA to determine whether the hot-water runoff from a particular power plant located near a large gulf is having an adverse effect on the marine life in the area. The biologist’s goal is to acquire a prediction equation for the number of marine animals located
Refer to the International Journal of Foresting Engineering (Vol. 19, 2008) study of neck muscle activity patterns among forestry vehicle operators, Exercise 12.23. Recall that the researchers identified the key explanatory variables of y = the number of sustained low-level muscle activity (SULMA)
Periodically, software engineers must provide estimates of their effort in developing new software. In the Journal of Empirical Software Engineering (Vol. 9, 2004), multiple regression was used to predict the accuracy of these effort estimates. The dependent variable, defined as the relative error
Air pollution regulations for power plants are often written so that the maximum amount of pollution that can be emitted increases as the plant’s output increases. Assuming this is true, write a model relating the maximum amount of pollution permitted (in parts per million) to a plant’s output
An engineer has proposed the following model to describe the relationship between the number of acceptable items produced per day (output) and the number of work-hours expended per day (input) in a particular production process: y = β0 + β1x + β2x2 + ∈where y = Number of
Many service stations offer self service gasoline at reduced prices when customers pay with cash rather than credit. Suppose an oil company wants to model the mean monthly gasoline sales, E(y), of its affiliated stations as a function of the type of service they offer: cash only, cash or credit
Refer to The Astronomical Journal (July 1995) study of quasars detected by a deep space survey, Exercise 11.72. Recall that several quantitative independent variables were used to model the quasar characteristic, rest frame equivalent width (y). The data for 25 quasars are saved in the QUASAR file.
Refer to the Statistics in Action problem for this chapter. Recall that we built a model for y = natural logarithm of supply price for an intrastate trucking shipment as a function of the following independent variables: x1 = Distance shipped (hundreds of miles), x2 = Weight of product shipped
A 40-year-old masonry duplex structure has recently undergone a passive solar retrofit with features including insulated exterior walls, heat distribution systems, storm sashes, and air-lock entries. To gauge the effectiveness of the improvements, architectural engineers monitored the winter energy
A company is studying three different safety programs, A, B, and C, in an attempt to reduce the number of work-hours lost because of accidents. Each program is to be tried at three of the company’s nine factories. The plan is to monitor the lost work-hours, y, for a 1-year period beginning 6
A field experiment was conducted to assess the effect of organic enrichment on the mean density of mosquito larvae. (Journal of the American Mosquito Control Association, June 1995.) Larval specimens were collected from a pond 3 days after the pond was flooded with canal water. A second sample of
Refer to the American Scientist (Jul–Aug. 1998) study of the relationship between number of self avoiding and unrooted walks, Exercise 11.71. The data for the analysis are repeated in the accompanying table.a. Give the equation relating the coded variable u to walk length, x, using the coding
The dissolved oxygen content, y, in rivers and streams is related to the amount, x1, of nitrogen compounds per liter of water and the temperature, x2, of the water. Write the complete second-order model relating E(y) to x1 and x2.
When the U.S. airline industry was deregulated, researchers have questioned whether the deregulation has ensured a truly competitive environment. If so, the profitability of any major airline would be related only to overall industry conditions (e.g, disposable income and market share) but not to
A firm has developed a new type of halogen lightbulb and is interested in evaluating its performance to decide whether to market the bulb. It is known that the level of light output of the bulb depends on the cleanliness of its surface area and the length of time the bulb has been in operation. The
In a designed experiment, a. What two factors affect the quantity of information?b. How does blocking increase the quantity of information?
According to a University of Florida researcher, the longer a beachgoers sits in wet sand or stays in the water, the higher the risk of gastroenteritis (University of Florida News, Jan. 29, 2008). The result is based on a study of over 1,000 adults conducted at three popular Florida beaches. The
Refer to the Journal of Articles in Support of the Null Hypothesis (Vol. 6, 2009) study to determine whether video game players have superior visual attention skills over non-video game players, Exercise 1.3. Recall that each in a sample of 65 male students was classified as a video game player or
Applied Animal Behaviour Science (October 2000) published a study of the taste preferences of caged cockatiels. A sample of birds bred at the University of California, Davis, was randomly divided into three experimental groups. Group 1 was fed purified water in bottles on both sides of the cage.
A University of South Florida clinical trial of 50,000 smokers was carried out to compare the effectiveness of CT scans with X-rays for detecting lung cancer. (Today’s Tomorrows, Fall 2002.) Each participating smoker was randomly assigned to one of two screening methods, CT or chest X-ray, and
Refer to the randomized block design setup to compare the mean costs estimated by four DOT engineers, Examples 13.2 and 13.3.a. Write the model for each observation of estimated cost y for engineer B. Sum the observations to obtain the average for engineer B.b. Repeat part a for engineer D.c. Show
The Electronic Journal of Biotechnology (Dec. 15, 2003) published an article on a comparison of two yeast extracts, baker’s yeast and brewer’s yeast. Brewer’s yeast is a surplus by-product obtained from a brewery, hence it is less expensive than primary grown baker’s yeast. Samples of both
Human Factors (December 2009) investigated whether back and knee strength dictates the load lifting strategies of males and females. A sample of 32 healthy adults (16 men and 16 women) participated in a series of strength tests on the back and the knees. Following the tests, the participants were
Factorial models.a. Write the complete factorial model for a 2 × 3 factorial experiment where both factors are qualitative.b. Write the complete factorial model for a 2 × 3 × 3 factorial experiment where the factor at two levels is quantitative and the other two factors are qualitative.
Consider a factorial design with two factors, A and B, each at three levels. Suppose we select the following treatment (factor–level) combinations to be included in the experiment: A1B1, A2B1, A3B1, A1B2, and A1B3.a. Is this a complete factorial experiment? Explain.b. Explain why it is impossible
Suppose you wish to investigate the effect of three qualitative factors on a response y.a. Explain why a factorial selection of treatments is better than varying each factor, one at a time, while holding the remaining two factors constant.b. Why is the randomized block design a poor design to use?
Why is replication important in a complete factorial experiment?
Consider a 2 × 2 factorial. How many replications are required to estimate the interaction β to within two units with a 95% confidence interval? Assume that the standard deviation of the response variable, y, is approximately 3.
For a randomized block design with b blocks, the estimated standard error of the estimated difference between any two treatment means is √2/b. Use this formula to determine the number of blocks required to estimate (μA - μB), the difference between two treatment means, to within 10 units using
How do you measure the quantity of information in a sample that is pertinent to a particular population parameter?
What steps in the design of an experiment affect the volume of the signal pertinent to a particular population parameter?
In what step in the design of an experiment can you possibly reduce the variation produced by extraneous and uncontrolled variables?
Explain the difference between a completely randomized design and a randomized block design. When is a randomized block design more advantageous?
Consider a two-factor factorial experiment where one factor is set at two levels and the other factor is set at four levels. How many treatments are included in the experiment? List them.
Write the complete factorial model for a 2 × 2 × 4 factorial experiment where both factors at two levels are quantitative and the third factor at four levels is qualitative. If you conduct one replication of this experiment, how many degrees of freedom will be available for estimating σ2?
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