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statistics for engineers and scientists

Probability And Statistics For Engineers 5th Edition Richard L Scheaffer, Madhuri Mulekar, James T McClave, Cecie Starr - Solutions

11.12 Calculate SSE and s 2 for the data of Exercise 11.7.Interpret s 2 value in context of problem.
11.13 Calculate SSE and s 2 for the data of Exercise 11.8.Interpret s 2 value in context of problem.
11.14 J. Matis and T.Wehrly (Biometrics, 35, no. 1, March 1979) report the data given in table below on the proportion of green sunfish that survive a fixed level of thermal pollution for varying lengths of time:a Fit the linear model by the method of least squares.b Plot the data points and graph
11.15 Refer to Exercise 11.1. Is there sufficient evidence to say that the slope of the line is significantly different from zero? Use .
11.16 Refer to Exercise 11.2. Estimate in a confidence interval with confidence coefficient 0.90.
11.17 Refer to Exercise 11.3. Estimate the amount of elongation per unit increase in force. Use a confidence coefficient of 0.95.
11.18 Refer to Exercise 11.4. Do industry sales appear to contribute any information to the prediction of company sales? Test at the 10% level of significance.
11.19 Refer to Exercise 11.5. Does Rockwell hardness appear to be linearly related to abrasion loss?use .
11.20 In Exercise 11.6, the price of a gallon of gasoline y was modeled as a function of the price of a barrel of crude oil x using the following equation:. Estimates of and were found to be 25.883 and 3.115, respectively.a Estimate the variance and standard deviation of .b Suppose the price of a
11.21 Refer to Exercise 11.7. Estimate the increase in expected number of parts assembled per 5-minute increase in time spent on the job. Use a 95% confidence coefficient.
11.22 Refer to Exercise 11.8. Does it appear that flowthrough LC50 values are linearly related to static LC50 values? Use .
11.23 It is well known that large bodies of water have a mitigating effect on the temperature of the surrounding land masses. On a cold night in central Florida, temperatures (in degrees Fahrenheit)were recorded at equal distances along a transect running in the downwind direction from a large
11.24 Refer to Exercise 11.1.a Estimate the mean value of Y for , using a 95% confidence interval.b Find a 95% prediction interval for a response Y at .
11.25 Refer to Exercise 11.3. Estimate the expected elongation for a force of 1.8, using a 90% confidence interval.
11.26 Refer to Exercise 11.4. If in 1988 the industry sales figure is 16, find a 95% prediction interval for the company sales figure. Do you see any possible difficulties with the solution to this problem?
11.27 Refer to Exercise 11.5. Estimate, in a 95% confidence interval, the mean abrasion loss for steel specimens with a Rockwell hardness measure of 75. What assumptions are necessary for your answer to be valid?
11.28 Refer again to Exercise 11.5. Predict, in a 95%prediction interval, the abrasion loss for a particular steel specimen with a Rockwell hardness measure of 75. What assumptions are necessary for your answer to be valid?
11.29 Refer to Exercise 11.7. Estimate, in a 90% confidence interval, the expected number of parts assembled by employees working for 12 minutes.
11.30 Refer to Exercise 11.8. Find a 95% prediction interval for a flow-through measurement corresponding to a static measurement of 21.0.
11.31 Refer to Exercise 11.3. If no force is applied, the expected elongation should be zero (that is,). Construct a test of versus, using the data of Exercise 11.3. Use.
11.32 In planning for an initial orientation meeting with new electrical engineering majors, the chairman of the Electrical Engineering Department wants to emphasize the importance of doing well in the major courses in getting better-paying jobs after graduation. To support this point, the chairman
11.33 Lawton (Journal of Pressure Vessel Technology, 2003) describes experiments conducted to determine temperature and heat transfer at the bore surface of the barrel at or near the commencement of rifling and to support the assessment of new ammunition for the 155 mm gun. The wear rate of
11.34 The yield pressure of an autofrettaged cannon is controlled by the applied and residual stresses in the cannon and by its material strength.Unanticipated yielding of cannon (or any other pressure vessel) can be a safety hazard.Underwood. Monk, Audino, and Parker (Journal of Pressure Vessel
11.35 Suppose that you fit the model Y = Bo+ Bx + B2x2 + Baxx2 + B4x + Bx + & to n = 30 data points and that SSE = 0.37 and R2 = 0.89 a Do the values of SSE and R suggest that the model provides a good fit to the data? Explain. b Is the model of any use in predicting y? Test the null hypothesis
11.36 In hopes of increasing the company’s share of the fine-food market, researchers for a meat-processing firm that prepares meats for exclusive restaurants are working to improve the quality of its hickory-smoked hams. One of their studies concerns the effect of time spent in the smokehouse on
11.37 Because the coefficient of determination R2 never decreases when a new independent variable is added to the model, it is tempting to include many variables in a model to force R2 to be near 1. However, doing so reduces the degrees of freedom available for estimating , which adversely affects
11.38 A utility company of a major city reported the average utility bills listed in the table below for a standard-size home during the last year.a Plot the points in a scatterplot.b Use the methods of Chapter 9 to fit the model What do you conclude about the utility of this model?c Hypothesize
11.39 To run a manufacturing operation efficiently, it is necessary to know how long it takes employees to manufacture the product. Without such information, the cost of making the product cannot be determined. Furthermore, management would not be able to establish an effective incentive plan for
11.40 A researcher wanted to investigate the effects of several factors on production-line supervisors’attitudes toward handicapped workers. A study was conducted involving 40 randomly selected supervisors. The response Y, a supervisor’s attitude toward handicapped workers, was measured with a
11.41 To project personnel needs for the Christmas shopping season, a department store wants to project sales for the season. The sales for the previous Christmas season are an indication of what to expect for the current season. However, the projection should also reflect the current economic
11.42 Suppose you fit the second-order model to data points. Your estimate of ‚ is and the standard error of the estimate is sbN 2 = 0.13.bN 2 = 0.35, n = 30 b2 Y = b0 + b1x + b2x 2 + e bN 2 = 0.55 sbN 2 = 0.181 bN 1 = 0.62 sNb 1 = 0.273 y = sales for upcoming Christmas x2 = sales for August of
11.43 How is the number of degrees of freedom available for estimating (the variance of ) related to the number of independent variables in a regression model?
11.44 An employer has found that factory workers who are with the company longer tend to invest more in a company investment program per year than workers who have less time with the company.The following model is believed to be adequate in modeling the relationship of annual amount invested Y to
11.45 Automobile accidents result in a tragic loss of life and, in addition, represent a serious dollar loss to the nation’s economy. Shown in the Table 11.3 are the number of highway deaths (to the nearest hundred) and the number of licensed vehicles(in hundreds of thousands) for the years
11.46 If producers (providers) of goods (services) are able to reduce the unit cost of their goods (services)by increasing the scale of their operation, they are the beneficiaries of an economic force known as economies of scale. Economies of scale cause a firm’s long-run average costs to decline
11.49 Suppose you fit the regression model to n 25 data points and you want to test the null hypothesis .a Explain how you would find the quantities necessary for the F-statistic.b How many degrees of freedom would be associated with F ?
11.50 An insurance company is experimenting with three different training programs, A, B, and C, for its salespeople. The following main effects model is proposed:where Y monthly sales (in thousands of dollars)x1 number of months of experience Training program A is the base level.a What
11.51 A large research and development company rates the performance of each of the members of its technical staff once a year. Each person is rated on a scale of zero to 100 by his or her immediate supervisor, and this merit rating is used to help determine the size of the person’s pay raise for
11.52 In an attempt to reduce the number of work hours lost due to accidents, a company tested each of three safety programs, A, B, and C, at three of the company’s nine factories. The proposed complete model is E(Y ) = b0 + b1x1 + b2x2 + b3x3 where Y total work hours lost due to accidents for
11.53 The following model was proposed for testing salary discrimination against women in a state university system:where Y annual salary (in thousands of dollars)x2 experience (years)Below is a portion of the computer printout that results from fitting this model to a sample of 200 faculty
11.54 A reactor pressure vessel is usually clad in stainless steel to prevent corrosion and radiation embrittlement. Thus, the occurrence of subclad cracks is higher than that of surface cracks. Kim et al. (Transactions of the ASME, 2003) performed 3-D elastic-plastic finite element analysis to
11.55 Table 11.6 gives the national air-quality data for the years 1980–2000 (National Air Quality and Emissions Report, 2003). All values are measured in ppm.a Plot the air quality data versus year. Describe any trends observed in the air quality measurements over the years data were collected.b
11.56 Stay and Barocas (International Journal for Numerical Methods in Fluids, 2003) demonstrated a localized reduction technique called“stitching” for hydrodynamic problems for which known analytical solution is available. They discussed the computational advantage of the coupled
11.57 The use of the variable-orifice damper has blossomed in Japan. These dampers provide a mechanically simple and low-power consumer means to protect structures against natural disaster by reducing structural vibrations. Spencer and Nagarajaiah (Journal of Structural Engineering, 2003) give the
11.58 Moles et al. (Chemical Engineering Research and Design, 2003) studied how computation times of the stochastic methods are reduced using parallelization (parallel implementation of different global optimization methods).a Make a scatterplot. Speed-up is measured as percent increase in
11.59 Wang and Reinhardt (Journal of Pressure Vessel Technology, 2003) studied the assessment of a steam generator tube. They analyzed a finite element model with a percentage degraded area(PDA) in the range of 10% to 90% and recorded the finite element limit load. The following table gives the PDA
11.60 Carrasco and Uribeotxeberria (IEE Proceedings Communications, 2003) recorded the total number of operations per input pattern required to implement two different algorithms, (SRK and RTRL) for different number of receiving antenna elements. They are reported in the table below.a Make a
11.61 In the 1960s, promotion of underground utilities as an alternative to traditional overhead distribution began.The costs for two types of utilities differ, and the power company has to provide both estimates to the potential developer of the property. Stanford (Journal of Energy Engineering,
11.62 Olajossy, Gawdzik, Budner, and Dula (Trans IchemE, 2003) conducted an experiment of plant output and recorded the ratio of recycled methane to feed methane. They also recorded the product purity (vol. %) and efficiency of methane recovery(%). The data are given in the table below.a Make
11.63 Rohner and Newmann (Transactions of the ASME, 2003) recorded the percentage of deviation of UV temperatures from black body temperatures.Two sets of data were collected, one based on the calibration at 1400C and the other at 1500C. The data are given in the table below.a Make a scatterplot of
11.64 Spath and Amos (Journal of Solar Energy Engineering, 2003) studied the process of hydrogen production via thermal decomposition of methane, using a solar reactor. The table on page 664 shows the hydrogen production rate, Y (in mol/s) at different solar irradiance, X (in w/m2) for 70%
11.65 Brittorf and Kresta (Trans IchemE, 2003) conducted experiments for solid-liquid mixing in stirred tanks and studied cloud height for solidsuspensions. They recorded the off-bottom clearance and impeller diameter, and measured the core velocity in water. Develop a model to predict the core
11.66 After a regression model is fit to a set of data, a confidence interval for the mean value of Y at a given setting of the independent variables will always be narrower than the corresponding prediction interval for a particular value of Y at the same setting of the independent variables.Why?
11.67 Before a particular job is accepted, a computer at a major university estimates the cost of running the job to see whether the user’s account contains enough money to cover the cost. As part of the job submission, the user must specify estimated values for two variables: central processing
11.68 Refer to Exercise 11.67 and the portion of the SAS printout shown in Figure 11.62 a Is there evidence that the model is useful(as a whole) for predicting job cost? Test at.b Is there evidence that the variables and interact to affect Y? Test at .c What assumptions are necessary for the tests
11.69 Refer to Exercise 11.67 and the portion of the SAS printout shown. Use a 95% confidence interval to estimate the mean cost of computer jobs that require 42 seconds of CPU time and print 2,000 lines.
11.70 Several states now require all high school seniors to pass an achievement test before they can graduate. On the test, the seniors must demonstrate their familiarity with basic verbal and mathematical skills. Suppose the educational testing company that creates and administers these exams
11.71 Refer to Exercise 11.70. The same data are now used to fit the model Thus, we now add the interaction between IQ and SES to the model. The SAS printout for this model is shown in Figure 11.64.a Identify the least-squares prediction equation.b Interpret the value of and test to determine
11.72 The EPA wants to model the gas mileage rating Y of automobiles as a function of their engine size x. A quadratic model Y = b0 + b1x + b2x2 R2+ b4x1x2 + b5x1x3 E(Y ) = b0 + b1x1 + b2x2 + b3x3(x2 = 0, x3 = 1)is proposed. A sample of 50 engines of varying sizes is selected, and the miles per
11.73 To increase the motivation and productivity of workers, an electronics manufacturer decides to experiment with a new pay incentive structure at one of two plants. The experimental plan will be tried at plant A for six months, while workers at plant B will remain on the original pay plan.To
11.74 One fact that must be considered in developing a shipping system that is beneficial to both the customer and the seller is time of delivery.A manufacturer of farm equipment can ship its products by either rail or truck. Quadratic models are thought to be adequate in relating time of delivery
11.75 Refer to Exercise 11.74. Suppose the proposed second-order model is fit to a total of 50 observations on delivery time. The sum x2 = distance to be shipped x1 = b 1 if rail 0 if truck Y = shipping time E(Y ) = b0 + b1x1 + b2x2 + b3x1x2 + b4x2 2 bN 2b2 a = 0.01 sb N 1 = 0.231 sb N 2 = 0.48 yN
11.76 Operations management is concerned with planning and controlling those organizational functions and systems that produce goods and services (Schroeder, Operations Management:Decision Making in the Operations Function, McGraw-Hill, 1981). One concern of the operations manager of a production
11.77 Many companies must accurately estimate their costs before a job is begun in order to acquire a contract and make a profit. For example, a heating and plumbing contractor may base cost estimate for new homes on the total area of the house, the number of baths in the plans, and whether central
11.78 Refer to Exercise 11.77. The contractor samples 25 recent jobs and fits both the complete second-order model part (b) and the reduced main effects model in part (a) so that a test can be conducted to determine whether the additional complexity of the second-order model is necessary. The
11.79 A company that services two brands of microcomputers would like to be able to predict the amount of time it takes a service person to perform preventive maintenance on each brand.It believes the following predictive model is appropriate:Y = b0 + b1x1 + b2x2 + e SSE R2 First-order 8.548 0.950
11.80 Many colleges and universities develop regression models for predicting the grade-point average(GPA), y, of incoming freshmen. This predicted GPA can then be used to help make admission decisions. Although most models use many independent variables to predict GPA, we will illustrate by
11.81 Refer to Exercise 11.80. Now fit the following second-order model to the data:a Interpret the value of , and test whether the data indicate that this model is useful for predicting freshman GPA. Use .b Sketch the relationship between predicted GPA and the verbal score x1 for the following
11.82 Plastics made under different environmental conditions are known to have differing strengths.A scientist would like to know which combination of temperature and pressure yields a plastic with a high breaking strength. A small preliminary experiment was run at two pressure levels and two
11.83 Air pollution regulations for power plants are often written so that the maximum amount of pollutant that can be emitted is increased as the plant’s output increases. Suppose the data in the table below are collected over a period of time:a Plot the data in a scatterplot.b Use the
11.84 The recent expansion of U.S. grain exports has intensified the importance of the linkage between the domestic grain transportation system and international transportation. As a first step in evaluating the economies of this interface, Martin and Clement (Transportation Journal, 1982) used
11.85 An economist has proposed the following model to describe the relationship between the number of items produced per day (output) and the number of hours of labor expended per day (input) in a particular production process:where Y number of items produced per day x number of hours of labor
11.86 An operations engineer 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).He has proposed the following model:where x1 age of
11.87 Refer to Exercise 11.86. The data that were used to fit the operations engineer’s complete and reduced models are displayed in table below.a Use these data to test the null hypothesis that in the complete model. Test by using .b Carefully interpret the results of the test in the context of
11.88 Refer to Exercise 11.45, where we presented data on the number of highway deaths and the number of licensed vehicles on the road for the years 1950–1979. We mentioned that the number of deaths Y may also have been affected by the existence of the national 55-mile-per-hour speed limit during
11.89 In Exercise 11.45, we fit a second-order model to data relating the number Y of U.S. highway deaths per year to the number x1 of licensed vehicles on the road. In Exercise 11.88, we added a qualitative variable x2 to account for the presence or absence of the 55-mile-per-hour national speed
11.90 Productivity has been defined as the relationship between inputs and outputs of a productive system.In order to manage a system’s productivity, it is necessary to measure it. Productivity is typically measured by dividing a measure of system out put by a measure of the inputs to the
11.91 The U.S. Federal Highway Administration publishes data on reaction distance for drivers andbraking distance for a typical automobile traveling on dry pavement. Some of the data appear in the table below. Total stopping distance is the sum of reaction distance and braking distance. Find simple
11.92 In building a model to study automobile fuel consumption, Biggs and Akcelik (Journal of Transportation Engineering, 1987) began by looking at the relationship between idle fuel consumption and engine capacity. Suppose the data are as shown in table below.What model do you think best explains
11.93 One important feature of the plates used in high-performance thin-layer chromatography is the water uptake capability. Six plates were modified by increasing the amount of cyanosilane(CN). Water uptake measurements (Rf) were then recorded for three component mixtures(BaP, BaA, Phe) used with
11.94 Low temperatures on winter nights in Florida have caused extensive damage to the state’s agriculture.Thus, it is important to be able to predict freezes quite accurately. In an attempt to use satellite data for this purpose, a study was done to compare the surface temperatures detected by
12.8 It has been hypothesized that treatment (after casting) of a plastic used in optic lenses will improve wear. Four different treatments are to be tested. To determine whether any differences in mean wear exist among treatments, 28 castings from a single formulation of the plastic were made, and
12.9 The application of management by objectives(MBO), a method of performance appraisal, was the object of a study by Shetty and Carlisle of Utah State University (“Organizational Correlates of a Management by Objectives Program,”Academy of Management Journal, 1974). The study dealt with the
12.10 The concentration of a catalyst used in producing grouted sand is thought to affect its strength. An experiment designed to investigate the effects of three different concentrations of the catalyst utilized five specimens of grout per concentration.The strength of a grouted sand was
12.11 Several companies are experimenting with the concept of paying production workers (generally paid by the hour) on a salary basis. It is believed that absenteeism and tardiness will increase under this plan, yet some companies feel that the working environment and overall productivity will
12.12 One of the selling points of golf balls is their durability. An independent testing laboratory is commissioned to compare the durability of three different brands of golf balls. Balls of each type will be put into a machine that hits the balls with the same force that a golfer uses on the
12.13 Eight independent observations on percent copper content were taken on each of four castings of bronze. The sample means for each casting are given in the table below.Is there sufficient evidence to say that there are differences among the mean percentages of copper for the four castings? Use
12.14 Three thermometers are used regularly in a certain laboratory. To check the relative accuracies of the thermometers, they are randomly and independently placed in a cell kept at zero degrees Celsius. Each thermometer is placed in the cell four times, with the results (readings in degrees
12.15 Casts of aluminum were subjected to four standard heat treatments and their tensile strengths were measured. Five measurements were taken on each treatment, with the results (in 1,000 psi), shown below.Perform an analysis of variance. Do the mean tensile strengths differ from treatment to
12.16 How does flextime, which allows workers to set their individual work schedules, affect worker job satisfaction? Researchers recently conducted a study to compare a measure of job satisfaction for workers, using three types of work scheduling:flextime, staggered starting hours, and fixed
12.17 Refer to Exercise 12.5. Answer part (b) by writing the appropriate linear model and using regression techniques.
12.18 Refer to Exercise 12.7. Test the assumption of equal percentages of kill for the four rates of application by writing a linear model and using regression techniques.
12.19 Refer to Exercise 12.14. Write a linear model for this experiment. Test for significant differences among the means for the three thermometers by using regression techniques.
12.20 Refer to Exercise 12.5.a Find a 90% confidence interval for .Interpret the interval.b What would happen to the width of the confidence interval in part (a) if you quadrupled the number of observations in the two samples?c Find a 95% confidence interval for .d Approximately how many
12.21 Refer to Exercise 12.6.a Suppose 3.7 and 4.1. Do the data provide sufficient evidence to indicate a difference between and ? Assume that there are seven observations for each treatment.Test by using 0.10.b Refer to part (a). Find a 90% confidence interval for .c Refer to part (a). Find
12.22 Refer to Exercise 12.7.a Estimate the true difference in mean percentage of kill between rate 2 and rate 5. Use a 90% confidence interval.b Construct confidence intervals for the six possible differences between treatment means, with simultaneous confidence coefficient close to 0.90.
12.23 Refer to Exercise 12.10.a Find a 95% confidence interval for the difference in mean strength for specimens produced with a 35% concentration of catalyst versus those containing a 45% concentration of catalyst.b Construct confidence intervals for the three treatment means, with simultaneous
12.24 Refer to Exercise 12.13. Casting 1 is a standard, and castings 2, 3, and 4 involve slight modifications to the process. Compare the standard with each of the modified processes by producing three confidence intervals with simultaneous confidence coefficient approximately 0.90.not matter which
12.29 A power plant that uses water from the surrounding bay for cooling its condensors is required by the EPA to determine whether discharging its heated water into the bay has a detrimental effect on the flora (plant life) in the water. The EPA requests that the power plant make its investigation
12.30 The Bell Telephone Company’s long-distance phone charges may appear to be exorbitant when compared with the charges of some of its competitors, but this is because a comparison of charges between competing companies is often analogous to comparing apples and eggs. Bell’s charges for

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