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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
Refer to Exercise 13.25. Write the model for y assuming that you wish to enter main effect terms for the factors, but no terms for factor interactions. How many degrees of freedom will be available for estimating σ2?Data from Exercise 13.25Write the complete factorial model for a 2 × 2 × 4
Researchers conducted an experiment to compare the mean job satisfaction rating E(y) of workers using three types of work scheduling: flextime (which allows workers to set their individual work schedules), staggered starting hours, and fixed hours.a. Identify the treatments in the experiment.b.
A commonly used index to estimate the reliability of a building subjected to lateral loads is the drift ratio. Sophisticated computer programs such as STAAD-III have been developed to estimate the drift ratio based on variables such as beam stiffness, column stiffness, story height, moment of
Suppose you plan to investigate the effect of hourly pay rate and length of workday on some measure y of worker productivity. Both pay rate and length of workday will be set at three levels, and y will be observed for all combinations of these factors.a. What type of experiment is this?b. Identify
A study was conducted to compare market shares of diesel engine brands estimated by two different auditing methods.a. Identify the treatments in the experiment.b. Because of brand-to-brand variation in estimated market share, a randomized block design will be used. Explain how the treatments might
Researchers investigated the effect of gender (male or female) and weight (light or heavy) on the length of time required by firefighters to perform a particular firefighting task (Human Factors). Eight firefighters were selected in each of the four gender–weight categories. Each firefighter was
The Journal of Testing and Evaluation (July 1992) published an investigation of the mean compression strength of corrugated fiberboard shipping containers. Comparisons were made for boxes of five different sizes: A, B, C, D, and E. Twenty identical boxes of each size were tested and the peak
Trends in Biomaterials & Artificial Organs (Jan. 2003) published a study of a new bonding adhesive for teeth. The new adhesive (called “Smart bond”) has been developed to eliminate the necessity of a dry field. In one portion of the study, 30 extracted teeth were bonded with Smart bond and
Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of gas turbines augmented with high-pressure inlet fogging, Exercise 8.39. Recall that the researchers classified gas turbines into three categories—traditional, advanced, and aero derivative—and measured the heat
Refer to the JOM (Jan. 2003) study of a new high-strength aluminum alloy for use in antisubmarine aircraft, tankers, and long-range bombers, Exercise 7.43. Recall that the new alloy is obtained by applying a retrogression and re aging (RAA) heat treatment to the current strongest aluminum alloy.
Hand rehabilitation systems that use virtual reality (VR) technology have been developed for patients with disabled hands and arms. In Robotica (Vol. 22, 2004), mechanical and systems engineers assessed the effectiveness of display devices for three VR-based hand rehabilitation systems. System A
Refer to the American Journal of Science (Jan. 2005) study of the chemical makeup of buried tills (glacial drifts) in Wisconsin, Exercise 2.22. The ratio of the elements aluminum (Al) and beryllium (Be) in sediment is related to the duration of burial. Recall that the Al/Be ratios for a sample of
A low cost and highly productive bio-fuel production method is high temperature fermentation. However, heat stress can inhibit the amount of ethanol produced during the process. In Engineering Life Sciences (March 2013), biochemical engineers carried out a series of experiments to assess the effect
Unlike most other commonly used engineering materials, concrete experiences a characteristic marked increase in “creep” when it is heated for the first time under load. To investigate this phenomenon, a study of the thermal strain behavior of concrete was conducted (Magazine of Concrete
Refer to the Marine Technology (Jan. 1995) study of major ocean oil spills by tanker vessels, Exercise 2.85. The spillage amounts (thousands of metric tons) and cause of accident for 48 tankers are saved in the OILSPILL file. (Note: Delete the two tankers with oil spills of unknown causes.) Conduct
The Perth (Australia) Metropolitan Water Authority recently completed construction of a land pipeline for transporting domestic wastewaters from a primary treatment plant. During construction, the cement mortar lining of the pipeline was tested for cracking to determine whether autogenous healing
Prior to shipping and during storage, citrus fruit stacked on pallets are susceptible to damage from high temperatures. Consequently, containers have been designed to keep the fruit cool. The Journal of Food Engineering (September 2013) published an article that investigated the cooling performance
Traditionally, solders used in electronics assembly are made with lead. Due to numerous environmental hazards associated with lead solders (e.g., groundwater contamination and breathing in of fine lead-bearing particles), engineers are developing lead-free solders. In Soldering & Surface Mount
A plant that manufactures denim jeans in the United Kingdom recently introduced a computerized automated handling system. The new system delivers garments to the assembly line operators by means of an overhead conveyor. While the automated system minimizes operator handling time, it inhibits
Refer to the Electronic Journal of Biotechnology (Dec. 15, 2003) study of two yeast extracts, baker’s yeast and brewer’s yeast, Exercise 13.10. Recall that samples of both yeast extracts were prepared at four different temperatures (45°, 48°, 51°, and 54°C), and the autolysis yield
Refer to the Robotica (Vol. 22, 2004) study of the effectiveness of display devices for three virtual reality (VR)-based hand rehabilitation systems, Exercise 14.10 (p. 756). Display device A is a projector, device B is a desktop computer monitor, and device C is a head-mounted display. Recall that
The use of coated cutting tools to machine various materials is considered state-of-the art technology. The impact of cutting tool coating and material on cutting force was investigated in an article published in the International Journal of Engineering and Applied Sciences (Vol. 7, 2011). Five
Mussel larvae are in great abundance in the drift material that washes up on Ninety Mile Beach in New Zealand. These larvae tend to settle on algae. Environmentalists at the University of Auckland investigated the impact of algae type on the abundance of mussel larvae in drift material.
The chemical element antimony is sometimes added to tin–lead solder to replace the more expensive tin and to reduce the cost of soldering. A factorial experiment was conducted to determine how antimony affects the strength of the tin–lead solder joint (Journal of Materials Science, May 1986).
A vegetation height of greater than 30 centimeters on a highway right of- way is generally considered a safety hazard to drivers. How often and at what height should the right-of-way be mowed in order to maintain a safe environment? This was the question of interest in an article published in the
As part of a study on the rate of combustion of artificial graphite in humid air flow, researchers conducted an experiment to investigate oxygen diffusivity through a water vapor mixture. A 3 × 9 factorial experiment was conducted with mole fraction of water (H2O) at three levels and temperature
Computer mediated communication (CMC) is a form of interaction that heavily involves technology (e.g., instant messaging, e-mail). Refer to the Journal of Computer-Mediated Communication (Apr. 2004) study to compare relational intimacy in people interacting via CMC to people meeting face-to-face
The Brazilian Journal of Chemical Engineering (Vol. 22, 2005) published a study to compare two foaming agents in the flotation of sulfured copper materials process. The two agents were surface-active bio oil (SABO) and pine oil (PO). A 2 × 2 × 2 × 2 factorial design was used to investigate the
An experiment was conducted to investigate the effects of three factors—paper stock, bleaching compound, and coating type—on the whiteness of fine bond paper. Three paper stocks (factor A), four types of bleaches (factor B), and two types of coatings (factor C) were used for the experiment. Six
Chemical modification of natural rubber is used to increase the rubber’s resistance to weathering. Cardanol, an agricultural byproduct of the cashew industry, is often grafted onto natural rubber for this purpose. Chemical engineers investigated a new method of grafting cardanol onto natural
The factors that impact the quality of manufactured medical wires used in cardiovascular devices was investigated in Quality Engineering (Vol. 25, 2013). A complete 3-factor factorial design, with each factor at 2 levels, was employed. The three factors (levels) are: Machine type (I or II),
Refer to Exercise 14.43. Since charging time is a quantitative factor, we could plot the strength y versus charging time x1 for each of the four combinations of alloy type and material condition. This suggests that a prediction equation relating mean strength E(y) to charging time x1 may be
Refer to Exercises 14.43–14.44. If the relationship between mean strength E(y) and charging time x1 is the same for all four combinations of alloy type and material condition, the appropriate model for E(y) isE(y) = β0 + β1x1 + β2x12Fit this model to the data. Use the regression results,
A 2 × 2 factorial experiment was conducted for each of 3 weeks to determine the effect of two factors, temperature and pressure, on the yield of a chemical. Temperature was set at 300° and 500°. The pressure maintained in the reactor was set at 100 and 200 pounds per square inch. Four days were
Large highwall failures at a strip mine in Queensland, Australia, occur by the sliding of soft, black bands of clay, called black clay planes, near the base of the highwall. A study was conducted to determine whether the chemical and mineralogical properties of the black clay planes are similar to
A two-stage nested sampling design was used to collect data to estimate the mean porosity of paper emerging from a paper machine. Ten patches of paper were randomly selected from the end of the paper roll, and four porosity readings were made on each. The data are shown in the following table.a.
Quality control engineers at DuPont utilize nested sampling schemes to determine the percentage of a product shipped that conforms to specifications.* First, a random sample of n1 production lots is selected; then, a random sample of n2 batches is selected from each production lot. Finally, n3
An experiment was conducted to estimate the mean level of sulfur content in coal produced by a particular mine. Five days were randomly selected and identified as coal sampling days. On each day, five coal cars were randomly selected and portions of coal were removed from each. Two specimens were
An experiment was conducted to monitor the resistivity of silicon mono crystals. The original data were collected according to a two-stage nested sampling design in which random samples of eight crystals were selected from among 30 lots. The measured resistivity of the crystals is recorded in the
The strength of paper depends upon the length and other characteristics of the wood fiber stock entering the paper machine. Consequently, as the source of the fiber stock varies over time, we expect the strength of the produced paper to vary also. To test this theory, 6 days were randomly selected
Refer to the Nature (Aug. 2000) study of robots trained to behave like ants, Exercise 14.4. Multiple comparisons of mean energy expended for the four colony sizes were conducted using an experiment wise error rate of .05. The results are summarized in the table.a. How many pairwise comparisons are
Whole wheat breads contain a high amount of phytic acid, which tends to lower the absorption of nutrient minerals. The Journal of Agricultural and Food Chemistry (Jan. 2005) published the results of a study to determine if sourdough can increase the solubility of whole wheat bread. Four types of
Refer to Exercise 14.34. Use a multiple comparisons procedure to compare the mean shear strengths for the four antimony amounts. Identify the means that appear to differ. Use α = .01.Data from Exercise 14.34The chemical element antimony is sometimes added to tin–lead solder to replace the more
Refer to the Landscape Ecology Journal (Jan. 2013) study of mowing effects on vegetation in highway rights-of-way, Exercise 14.35. Recall that a 3 × 3 factorial design was employed to estimate the effects of mowing frequency and mowing height on the mean height of vegetation. The researchers
Check the assumptions for the completely randomized ANOVA of Exercise 14.8.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, Exercise 8.39. Recall that the researchers classified gas
Check the assumptions for the completely randomized ANOVA of Exercise 14.11.Data from Exercise 14.11Refer to the American Journal of Science (Jan. 2005) study of the chemical makeup of buried tills (glacial drifts) in Wisconsin, Exercise 2.22. The ratio of the elements aluminum (Al) and beryllium
Check the assumptions for the completely randomized ANOVA of Exercise 14.13.Data from Exercise 14.13The drug scopolamine is often used as a sedative to induce sleep in patients. In Behavioral Neuroscience (Feb. 2004), medical researchers examined scopolamine’s effects on memory for word-pair
Check the assumptions for the randomized block ANOVA of Exercise 14.25.Data from Exercise 14.25Refer to the Journal of Bacteriology (July 2002) study of the sensitivity of bacteria genes to light, Exercise 8.49 (p. 406). Recall that scientists isolated 103 genes of the bacterium responsible for
Check the assumptions for the factorial design ANOVA of Exercise 14.34. Data from Exercise 14.34The chemical element antimony is sometimes added to tin–lead solder to replace the more expensive tin and to reduce the cost of soldering. A factorial experiment was conducted to determine
Check the assumptions for the factorial design ANOVA of Exercise 14.36.Data from Exercise 14.36A 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
An article in the American Journal of Political Science (Jan. 1998) examined the attitudes of three groups of professionals that influence U.S. policy. Random samples of 100 scientists, 100 journalists, and 100 government officials were asked about the safety of nuclear power plants. Responses were
Refer to the completely randomized design of Exercise 13.27. Recall that the researchers want to compare the mean job satisfaction rating of workers using three types of work scheduling: flextime, staggered starting hours, and fixed hours. Use the random number table (Table 1 in Appendix B) to
Speech recognition technology has advanced to the point that it is now possible to communicate with a computer through verbal commands. A study was conducted to evaluate the value of speech recognition in human interactions with computer systems (Special Interest Group on Computer-Human Interaction
The Journal of Hazardous Materials (July 1995) published the results of a study of the chemical properties of three different types of hazardous organic solvents used to clean metal parts: aromatics, chloroalkanes, and esters. One variable studied was sorption rate, measured as mole percentage.
An evaluation of diffusion bonding of zircaloy components is performed. The main objective is to determine which of three elements—nickel, iron, or copper— is the best bonding agent. A series of zircaloy components are bonded using each of the possible bonding agents. Since there is a great
A commonly used index to estimate the reliability of a building subjected to lateral loads is the drift ratio. Sophisticated computer programs such as STAAD-III have been developed to estimate the drift ratio based on variables such as beam stiffness, column stiffness, story height, moment of
Acid rain is considered by some environmentalists to be the nation’s most serious environmental problem. It is formed by the combination of water vapor in clouds with nitrogen oxide and sulfuric dioxide emissions from the burning of coal, oil, and natural gas. The acidity of rain in central and
What is the optimal method of directing newcomers to a specific location in a complex building? Researchers at Ball State University (Indiana) investigated this “wayfinding” problem and reported their results in Human Factors (Mar. 1993). Subjects met in a starting room on a multilevel building
The steam explosion of peat renders fermentable carbohydrates that have a number of potentially important industrial uses. A study of the steam explosion process was initiated to determine the optimum conditions for the release of fermentable carbohydrate (Biotechnology and Bioengineering, Feb.
As oil drilling costs rise at unprecedented rates, the task of measuring drilling performance becomes essential to a successful oil company. One method of lowering drilling costs is to increase drilling speed. Researchers at Cities Service Co. have developed a drill bit, called the PD-1, which they
Many temperate-zone animal species exhibit physiological and morphological changes when the hours of daylight begin to decrease during autumn months. A study was conducted to investigate the “short day” traits of collared lemmings (The Journal of Experimental Zoology, Sept. 1993). A total of
The percentage of water removed from paper as it passes through a dryer depends on the temperature of the dryer and the speed of the paper passing through it. A laboratory experiment was conducted to investigate the relationship between dryer temperature T at three levels and exposure time E (which
The data shown in the table below are the results of an experiment conducted to investigate the effect of three factors on the percentage of ash in coal. The three factors, each at four levels, were Type of coal (factor A): Mojiri, Michel, Kairan, and Metallurgical coke Maximum
A chemist has run an experiment to study the effect of four treatments on the glass transition temperature (in degrees Kelvin) of a particular polymer compound. Raw material used to make this polymer is bought in small batches. The material is thought to be fairly uniform within a batch but
Refer to Exercises 16.16 and 16.25 and the hourly data collected by BPI consulting. Conduct a runs analysis on both the x̅-chart and the R-chart. Interpret the results.Data from Exercise 16.16BPI Consulting, a leading provider of statistical process control software and training in the United
A computer lab at the University of Oklahoma is open 24 hours a day, 7 days a week. In Production and Inventory Management Journal (3rd Quarter, 1999), S. Barman investigated whether computer usage differed significantly (1) among the 7 days of the week and (2) among the 24 hours of the day. Using
A 2 × 2 × 2 × 2 = 24 factorial experiment was conducted to investigate the effect of four factors on the light output, y, of flashbulbs. Two observations were taken for each of the factorial treatments. The factors are: amount of foil contained in a bulb (100 and 120 milligrams); speed of
Refer to the Human Factors (Apr. 1990) study of recognizer accuracy at three levels (90%, 95%, and 99%) and vocabulary size at three levels (75%, 87.5%, and 100%) on the performance of a computerized speech recognizer, Exercise 12.26 (p. 661). The data on task completion times (minutes) were
Aroni and Fletcher (1979) presented data on the compressive and tensile strength of mortar used to line steel water pipelines. They noted that mortar strength is expected to increase as the curing time of the mortar increases from 7 to 28 days. The compressive and tensile strength means and
An experiment was conducted to determine the effect of sintering time (two levels) on the compressive strength of two different metals. Five test specimens were sintered for each metal at each of the two sintering times. The data (in thousands of pounds per square inch) are shown in the
Is the navigational behavior of cockroaches scavenging for food random or linked to a chemical trail? In an attempt to answer this question, an entomologist designed an experiment to test a cockroach’s ability to follow a trail of its fecal material (Explore, Research at the University of
Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the characteristics of cheek teeth (e.g., molars) in an extinct primate species, Exercise 2.14. Recall that the researchers measured the dentary depth of molars (in millimeters) for 18 cheek teeth extracted from
Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study on the current trend in the design of social robots, Exercise 7.33. Recall that in a random sample of social robots obtained through a web search, 28 were built with wheels. The number of wheels on each of the 28
Refer to the Environmental Science & Technology (Sept. 1, 2000) study of ammonia levels near the exit ramp of a San Francisco highway tunnel, Exercise 2.30. The daily ammonia concentrations (parts per million) on eight randomly selected days during afternoon drive-time are reproduced in the
Is text messaging the preferred option for students’ communication with their professor? This was the question of interest in a study published in Chemical Engineering Education (Spring 2012). Students in two sections of a chemical engineering class participated in the study. One section (18
Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of gas turbines augmented with high-pressure inlet fogging, Exercise 8.29. The data on engine heat rate (kilojoules per kilowatt per hour) is saved in the GASTURBINE file. Recall that the researchers classified gas
An experiment was conducted to study the effect of reinforced flanges on the torsional capacity of reinforced concrete T-beams (Journal of the American Concrete Institute, Jan.–Feb. 1986). Several different types of T-beams were used in the experiment, each type having a different flange width.
Refer to the Chance (Fall 2002) study of a patent infringement case brought against Intel Corp., Exercise 7.44. Recall that the case rested on whether a patent witness’s signature was written on top of key text in a patent notebook or under the key text. Using an X-ray beam, zinc measurements
Use the formula for the sum of an arithmetic progression to show thatfor the Wilcoxon rank sum test. n(n + 1) T + T, = 2
Show that for the special case where n1 = 2 and n2 = 2, the formula for the expected value of the Wilcoxon rank sum T2 given in this section holds. List the (n1 + n2)! = 4! ways that the ranks can be assigned, and compute T2 for each assignment. Then use the fact that the probability of any
Consider the Wilcoxon rank sum T1 for the case where n1= 3 and n2 = 3. Use the technique outlined in this section to find TL such that P(T1 ≤ TL) ≈ .05.
Refer to the National Highway Traffic Safety Administration (NHTSA) crash test data for new cars saved in the CRASH file. In Exercise 7.54. you compared the chest injury ratings of drivers and front-seat passengers using the Student’s T procedure for matched pairs. Suppose you want to make the
Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of gas turbines augmented with high-pressure inlet fogging, Exercise 15.14. The Kruskal–Wallis test was used to compare the heat rate distributions for traditional, advanced, and aero derivative gas turbine engines.
Refer to the Asian Journal of Industrial Engineering (Vol. 4, 2012) evaluation of a computerized mathematical model used in single machine batch scheduling, Exercise 10.27. Recall that the performance of the model was graded using a variable called Value of Object Function (VOF).Data on VOF, run
Refer to the Chemical Engineering Journal (April, 2013) study of a method for removing nitrogen from toxic wastewater, Exercise 10.53. Recall that the researchers related y = the amount of nitrogen removed (measured in milligrams per liter) from a wastewater specimen to x = the amount of ammonium
A certain airplane model is susceptible to alignment errors in the manufacturing process. To monitor this process, the total number of alignment errors observed at final inspection for each of the first 25 aircraft produced were recorded, as shown in the table, right column.a. Construct a c-chart
A company manufactures rolled steel for nuclear submarines. To monitor the production process, a quality control inspector sampled finished rolls of steel from the production line, one each hour for 12 consecutive hours. The number of imperfections discovered on each roll is recorded in the
Suppose y1, y2, ..... yn is a random sample from a normal distribution with unknown mean m and variance σ2 = 1, i.e.,Show that the likelihood L of the sample is 1 f(y) %3D V27
Show that for a fixed sample size n, α increases as decreases, and vice versa.
Suppose y is a random sample of size n = 1from a normal distribution with mean 0 and unknown variance σ2.a. Show that y2/σ2 has a chi-square distribution with 1 degree of freedom.b. Derive a 95% confidence interval for σ2 using y2/σ2 as a pivotal statistic.
Suppose y is a random sample of size n = 1 from a gamma distribution with parameters α = 1 and arbitrary β.a. Show that 2y/β has a gamma distribution with parameters α = 1 and β = 2.b. Use the result of part a to show that 2y/β has a chi square distribution with 2 degrees of freedom.c. Derive
Suppose y is a single observation from a normal distribution with mean μ and variance 1. Use y to find a 95% confidence interval for μ.
A confidence interval for θ is said to be unbiased if the expected value of the interval midpoint is equal to θ. a. Show that the small-sample confidence interval for μ,is unbiased.b. Show that the confidence interval for σ2, is biased. y - ta/2 Vn susỹ + ta/2 Vn
Suppose y is a single observation from a uniform distribution defined on the interval from 0 to θ. Find a 95% confidence limit LCL for θ such that P(LCL < θ < ∞) = .95. Start with the pivotal statistic y/θ and show (using the method of Chapter 6) that y/θ is uniformly distributed on
Define α and β for a statistical test of hypothesis.
Refer to Exercise 8.8 and 8.9. Show that the rejection region λ ≤ λα is equivalent to the rejection region y̅ ≥ y̅α, where P(λ ≤ λα) and P(y̅ ≥ y̅α) = α. Use the fact that e-a2 → 0 as |a| → ∞. Data from Exercise 8.8 Suppose y1, y2, ..... yn is a random sample from a
An article in ACS Sustainable Chemistry & Engineering (Vol. 1, 2013) investigated the use of natural fiber composites produced from switchgrass. Researchers want to know if the mean tensile strength of this fiber composite exceeds 20 megapascals.
A herpetologist wants to determine whether the egg-hatching rate for a certain species of frog exceeds .5 when the eggs are exposed to ultraviolet radiation.
A manufacturer of fishing line wants to show that the mean breaking strength of a competitor’s 22-pound line is really less than 22 pounds.
A technique, called matrix solid-phase dispersion (MSPD), has been developed for chemically extracting trace organic (toxic) compounds from fish specimens (chromatographia, Mar. 1995). Uncontaminated fish fillets were injected with a toxic substance and the MSPD method was used to extract the
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