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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
12.31 From time to time, one branch office of a company must make shipments to a certain branch office in another state. There are three package delivery services between the two cities where the branch offices are located. Since the price structures for the three delivery services are quite
12.32 Due to increased energy shortages and costs, utility companies are stressing ways in which home and apartment utility bills can be cut. One utility company reached an agreement with the owner of a new apartment complex to conduct a test of energy-saving plans for apartments. The tests were to
12.33 A chemist runs an experiment to study the effects of four treatments on the glass transition temperature 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 variable between
12.36 Refer to Exercise 12.25. Answer parts (b) and (c)by fitting a linear model to the data and using regression techniques.
12.37 Refer to Exercise 12.29. Answer part (a) by fitting a linear model to the data and using regression techniques.
12.38 Suppose that three automobile engine designs are being compared to determine differences in mean time between breakdowns.a Show how three test automobiles and three different test drivers could be used in a 3 3 Latin square design aimed at comparing the engine designs.b Write the linear
12.39 Refer to Exercise 12.27 a Form a 95% confidence interval to estimate the true mean difference in pressure between nickel and iron. Interpret this interval.b Form confidence intervals on the three possible differences between the means for the bonding agents, using a simultaneous confidence
12.40 Refer to Exercise 12.28. Use a 90% confidence interval to estimate the true difference between the mean responses given by estimators B and C.
12.41 Refer to Exercise 12.29. What are the significant differences among the station means? (Use a simultaneous confidence coefficient of 0.90.)
12.42 Refer to Exercise 12.30. Compare the three telephone companies’ mean rates by using a simultaneous confidence coefficient of approximately 0.90.
12.43 Refer to Exercise 12.31.a Use a 99% confidence interval to estimate the difference between the mean delivery times for carriers I and II.b What assumptions are necessary for the validity of the procedures you used in part (a)?
12.44 In pressure sintering of alumina., two important variables controlled by the experimenter are the pressure and time of sintering. An experiment involving two pressures and two times, with three specimens tested on each pressure/time, combination, showed the densities (in v/cc): listed in
12.45 The yield percentage Y of a chemical process depends on the temperature at which the process is run and the length of time the process is active. For two levels of temperature and two lengths of time, the yields are listed in table below (with two observations per treatment):a Perform an
12.46 The yield percentage Y of a certain precipitate depends on the concentration of the reactant and the rate of addition of diammonium hydrogen phosphate. Experiments were run at three different concentration levels and three addition rates. The yield percentages, with two observations per
12.47 How do women compare with men in their ability to perform laborious tasks that require strength?Some information on this question is provided in a study by Phillips and Pepper of the fire-fighting ability of men and women. (“Shipboard Fire-Fighting Performance of Females and Males,”Human
12.48 Refer to Exercise 12.47. Phillips and Pepper(1982) give data on another factorial experiment utilizing 20 males and 20 females. The experiment involved the same treatments, with ten persons assigned to each sex/weight category.The response measured for each person was the pulling force the
12.49 In analyzing coal samples for ash content, two types of crucibles and three temperatures were used in a complete factorial arrangement, with as listed in table below.(Two independent observations were taken on each treatment.) Note that “crucible” is not a quantitative factor, but it can
12.50 Four different types of heads were tested on each of two sealing machines. Four independent measurements of strain were then made on each head/machine combination. The data are given table below.a Perform an analysis of variance, making all appropriate tests at the 5% level of significance.b
12.51 An experiment was conducted to determine the effects of two alloying elements (carbon and manganese) on the ductility of specimens of metal. Two specimens from each treatment were measured, and the data (in work required to break a specimen of standard dimension) are listed in table below.a
12.52 Eisinger et al. (Transactions of the ASME, 2003)conducted laboratory scale model tests of one simulated stack liner exposed to airflow at ambient atmospheric conditions. The tests were conducted at three different flow velocities( m/s) to obtain baseline data and data with two and three guide
12.55 Mileage tests were performed to compare three different brands of unleaded gas. Four different automobiles were used in the experiment, and each brand of gas was used in each car until the mileage was determined.The results, in miles per gallon, are shown in the table below:a Is there
12.56 The following table shows the partially completed analysis of variance for a two-factor factorial experiment.d State the practical implications of your test results in part (c).
12.57 The data shown in the table below: are for a factorial experiment with two observations per factor-level combination.a Perform an analysis of variance for the data and display the results in an analysis of variance table.b Do the data provide sufficient information to indicate an interaction
12.58 The set of activities and decisions through which a firm moves from its initial awareness of an innovative industrial procedure to its final adoption or rejection of the innovation is referred to as the industrial adoption process. The process can be described as having five stages:(1)
12.59 England has experimented with different 40-hour workweeks to maximize, production and minimize expenses. A factory tested a 5-day week(8 hours per day), a 4-day week (10 hours per day), and a day week (12 hours per day), with the weekly production results shown in the c Is there evidence of a
12.60 To compare the preferences of technicians for three brands of calculators, each of three technicians was required to perform an identical series of calculations on each of the three calculators, A, B, and C. To avoid the possibility of fatigue, a suitable time period separated each set of
12.61 Sixteen workers were randomly selected to participate in an experiment to determine the effects of work scheduling and method of payment on attitude toward the job. Two types of scheduling were employed, the standard 8 to 5 workday and a modification whereby the worker was permitted to start
12.62 An experiment was conducted to compare the yields of orange juice for six different juice extractors. Because of a possibility of a variation in the amount of juice per orange from one truckload of oranges to another, equal weights of oranges from a single truckload were assigned to each
12.63 A farmer wants to determine the effect of five different concentrations of lime on the pH (acidity)of the soil on a farm. Fifteen soil samples are to be used in the experiment, five from each of the three different locations. The five soil samples from each location are then randomly assigned
12.64 In the hope of attracting more riders, a city transit company plans to have express bus service from a suburban terminal to the downtown business district. These buses should save travel time. The city decides to perform a study of the effect of four different plans (such as a special bus
12.65 Five sheets of writing paper are randomly selected from each of three batches produced by a certain company. A measure of brightness is obtained for each sheet, with the results listed in table below.a Do the mean brightness measurements seem to differ among the three batches? Use 0.05.b If
12.66 In order to provide its clients with comparative information on two large suburban residential communities, a realtor wants to know the average home value in each community. Eight homes are selected at random within each community and are appraised by the realtor. The appraisals are given in
12.67 Drying stresses in wood produce acoustic emissions(AE), and the rate of acoustic emission can be monitored as a check on drying conditions.The data shown in Table 12.18 are the results of measuring peak valued of acoustic emission over 10-second intervals for wood specimens with k = 2 a =H0:
12.68 In a study of wood-laminating adhesives by Kreibich and Hemingway (Forest Products Journal, 37(2), 1987, pp. 43–46), tannin is added to the usual phenol-resorcinolformaldehyde(PRF) resin and tested for strength. For four mixtures of resin and tannin and two types of test (test A, dry shear
12.69 Acid precipitation studies in southeastern Arizona involved sampling rain from two sites(Bisbee and the Tucson Research Ranch of the National Audubon Society) and sampling air from smelter plumes. The data for five elements, in terms of their ratios to copper, are given in the Table 12.19.
12.70 Lumber moisture content (MC) must he monitored during drying in order to maximize the lumber quality and minimize the drying coats.Four types of moisture meters were studied on three levels of moisture content in lumber by Breiner, Arganbright, and Pong (Forest Products Journal, 37(4), 1987,
12.78 Wet air oxidation is a technology used for treating wastewaters that are either too diluted to incinerate or too concentrated or toxic to biologically degrade. Oliviero et al. (Transactions of IChemE, 2003) recorded the concentrations of liquid phase reaction intermediates and time
12.79 Triano et al. (Transactions of the ASME, 2003)conducted uniaxial tension/compression tests on a servo-hydraulic test machine. Tests were run for four different materials at total strains of 1%, 2%, 3%, and 4%. The resulting Bauschinger modulus reduction (BMR) was recorded. The data is given
12.80 Zhao (Journal of Pressure Vessel Technology, 2003) performed fatigue tests on a servohydraulic machine at a temperature of 240°C, under total strain control, using a symmetrical push–pull triangular wave mode. Six total strain amplitudes were used and seven randomly assigned specimens were
10.1 The output voltage for a certain electric circuit is specified to be 130. An electrical engineer claims that in his experience these circuits produce less than 130 volts. He decides to take a random sample of independent readings to support his claim. Formulate null and alternative hypotheses
10.21 For a certain type of electronic surveillance system, the specifications state that the system will function for more than 1,000 hours with probability at least 0.90. Checks on 40 such systems show that 5 failed prior to 1,000 hours of operation. Does this sample provide sufficient a = 0.05 a
10.22 The hardness of a certain rubber (in degrees Shore) is claimed to be 65. Fourteen specimens are tested, resulting in an average hardness measure of 63.1 and a standard deviation of 1.4.Is there sufficient evidence to reject the claim, at the 5% level of significance? What assumption is
10.23 Certain rockets are manufactured with a range of 2,500 meters. It is theorized that the range will be reduced after the rockets are in storage for some time. Six of these rockets are stored for a certain period of time and then tested. The ranges found in the tests are as follows: 2,490,
10.24 For screened coke, the porosity factor is measured by the difference in weight between dry and soaked coke. A certain supply of coke is claimed to have a porosity factor of 1.5 kilograms.Ten samples are tested, resulting in a mean porosity factor of 1.9 kilograms and a variance of 0.04. Is
10.25 The stress resistance of a certain plastic is specified to be 30 psi. The results from 10 specimens of this plastic show a mean of 27.4 psi and a standard deviation of 1.1 psi. Is there sufficient evidence to doubt the specification at the 5%significance level? What assumption are you making?
10.26 Yield stress measurements on 51 steel rods with 10 mm diameters gave a mean of 485 N/mm2 and a standard deviation of 17.2. (See Booster, Journal of Quality Technology, 1983, for details.) Suppose the manufacturer claims that the mean yield stress for these bars is 490.Does the sample
10.27 The widths of contact windows in certain CMOS circuit chips have a design specification of 3.5(see Phadke et al., The Bell System Technical Journal, 1983, for details.) Postetch window widths of test specimens were as follows:3.21, 2.49, 2.94, 4.38, 4.02, 3.82, 3.30, 2.85, 3.34, 3.91 Can we
10.28 The variation in window widths for CMOS circuit chips must be controlled at a low level if the circuits are to function properly. Suppose specifications state that for window widths. Can we reject the claim that this specification is being met, using the data of Exercise 10.27? Use .
10.29 The Florida Poll of February–March 1984 interviewed 871 adults from around the state. On one question, 53% of the respondents favored strong support of Israel.Would you conclude that a majority of adults in Florida favor strong support of Israel? (Source: Gainesville Sun, April 1, 1984.)
10.30 A Yankelovich, Skelly, and White poll reported upon on November 30, 1984, showed that 54%of 2,207 people surveyed thought the U.S.income tax system was too complicated. Can we conclude safely, at the 5% significance level, that the majority of Americans think the income tax system is too
10.31 Wire used for wrapping concrete pipe should have an ultimate tensile strength of 300,000 pounds, according to a design engineer. Forty tests of such wire used on a certain pipe showed a mean ultimate tensile strength of 295,000 pounds and a standard deviation of 10,000. Is there sufficient
10.32 The break angle in a torsion test of wire used in wrapping concrete pipe is specified to be 40 degrees. Fifty torsion tests of wire wrapping a certain malfunctioning pipe resulted in a mean break angle of 37 degrees and a standard deviation of 6 degrees. Can we say that the wire used on the
10.33 Soil pH is an important variable in the design of structures that will contact the soil. The pH at a potential construction site was said to average 6.5. Nine test samples of soil from the site gave readings of 7.3, 6.5, 6.4, 6.1, 6.0, 6.5, 6.2, 5.8, 6.7 Do these readings cast doubt upon the
10.34 The resistances of a certain type of thermistor are specified to be normally distributed with a mean of 10,000 ohms and a standard deviation of 500 ohms, at a temperature of 25°C. Thus, only about 2.3% of these thermistors should produce resistances in excess of 11,000 ohms. The exact
10.35 The dispersion, or variance, of haul times on a construction project is of great importance to the project supervisor, because highly variable haul times cause problems in scheduling jobs.The supervisor of the truck crews states that the range of haul times should not exceed 40 minutes (The
10.36 Aptitude tests should produce scores with a large amount of variation so that an administrator can distinguish between persons with low aptitude and persons with high aptitude. The standard test used by a certain industry has been producing scores with a standard deviation of 5 points. A new
10.37 For the rockets of Exercise 10.23, the variation in ranges is also of importance. New rockets have a standard deviation of range measurements equal to 20 kilometers. Does it appear that storage increases the variability of these ranges?Use a = 0.05.
10.20 A manufacturer of resistors claims that 10% fail to meet the established tolerance limits. A random sample of resistance measurements for 60 such resistors reveals eight to lie outside the tolerance limits. Is there sufficient evidence to refute the manufacturer’s claim, at the 5%
10.19 The pH of water coming out of a certain filtration plant is specified to be 7.0. Thirty water samples independently selected from this plant show a mean pH of 6.8 and a standard deviation of 0.9.Is there any reason to doubt that the plant’s specification is being maintained? Use . Find the
10.18 For testing versus with, as in Exercises 10.16 and 10.17, find the sample size required for 0.01 and 0.05.
10.2 Refer to the situation in Exercise 10.1. Describe type I and type II errors that the engineer could possibly make.
10.3 The Rockwell hardness index for steel is determined by pressing a diamond point into the steel and measuring the depth of penetration.The manufacturer claims that this steel has an average hardness index of at least 64. A competitor decides to check out this claim. Formulate null and
10.4 Refer to Exercise 10.3.a What decision by the competitor could lead to a type I error?b What decision by the competitor could lead to a type II error?
10.5 The hardness of a certain rubber (in degrees Shore)is claimed to be 65 by the manufacturer. One of their customers suspects that the rubber produced by this manufacturer is not as hard as claimed. What null and alternative hypotheses should the customer use to test the manufacturer’s claim?
10.6 Refer to Exercise 10.5. Identify type I and type II errors that the customer could possibly make.
10.7 Certain rockets are manufactured with a range of 2,500 meters. It is theorized that the range will be reduced after the rockets are in storage for some time. Develop null and alternative hypothesis to support the theory by rocket scientists of a shorter range of rockets after storage.
10.8 Refer to Exercise 10.7. Describe type I and type II errors that the rocket scientists could possibly make.
10.9 The stress resistance of a certain plastic is specified to be 30 psi. A toy manufacturer uses this plastic. Recently, the toy manufacturer has received several complaints about the quality of toys and suspects lower than claimed stress resistance of the plastic.Formulate null and alternative
10.10 Refer to Exercise 10.9.a Describe type I and type II hypotheses that the toy manufacturer could possibly make.b Describe consequences of making such errors.
10.11 Steel rods with 10 mm diameters are used in the construction of bridges. The steel rods are used only if their yield stress exceeds 490. The state government is reviewing the product of one manufacturer to possibly use in the construction. The product will be tested before issuing a
10.12 Refer to the situation in Exercise 10.11.a Describe type I and type II hypotheses that the state government could possibly make.b Describe consequences of making such errors.
10.13 The output voltage for a certain electric circuit is specified to be 130. A sample of 40 independent readings on the voltage for this circuit gave a sample mean of 128.6 and a standard deviation of 2.1. Test the hypothesis that the average output voltage is 130 against the alternative that it
10.14 Refer to Exercise 10.13. If the voltage falls as low as 129, serious consequences may result. For testing versus , find , the probability of a Type II error, for the rejection region used in Exercise 10.13.
10.15 For testing versus with, as in Exercise 10.14, find the sample size that will yield and .
10.53 Gasoline mileage is to be compared for two automobiles, A and B, by testing each automobile on five brands of gasoline. Each car used one tank of each brand, with the following results (in miles per gallon):Is there evidence to suggest a difference between true average mileage figures for the
10.16 The Rockwell hardness index for steel is determined by pressing a diamond point into the steel and measuring the depth of penetration. For 50 specimens of a certain type of steel, the Rockwell hardness index averaged 62 with a standard deviation of 8. The manufacturer claims that this steel
10.17 Steel is sufficiently hard for a certain use as long as the mean Rockwell hardness measure does not drop below 60. Using the rejection region found in Exercise 10.16, find for the specific alternative
10.38 Two designs for a laboratory are to be compared with respect to the average amount of light produced on table surfaces. Forty independent measurements (in footcandles) are taken in each laboratory, with the following results:Is there sufficient evidence to suggest that the designs differ with
10.39 Shear-strength measurements derived from unconfined compression tests for two types of soils gave the following results (measurements in tons per square foot):Do the soils appear to differ with respect to average shear strength, at the 1% significance level? Soil Type I n = 30 Soil Type II n
10.80 The data in the following table show the frequency counts for 400 observations on the number of bacterial colonies within the field of a microscope, using samples of milk film.(Bliss and Owens, Biometrics, 1953.) Test the hypothesis that the data come from a Poisson distribution. Use 0.05.
10.62 Chitizadeh and Varghani (IEE Proceedings Communications, 2003) proposed a new crossbar switch with input queue. Crossbar switches are used for connecting multiple inputs to multiple outputs in a matrix manner. They are used in information processing applications such as packet switching as
10.63 In material sciences, measuring temperatures accurately is of great importance. Optical pyrometry is an established method used for measuring temperatures. These pyrometric temperature measurements are affected by selection of operating wavelength and atmospheric conditions. To solve some of
10.64 Pfeifer, Schubert, Liauw, and Emig (Trans IChemE, 2003) studied dynamic behavior of microreactors for methanol steam reforming, which is used in fuel cell applications. They measured temperatures on the top cover plate of reactor type RS2 at a set point of 310°C for two different electric
10.66 Two types of defects, A and B, are frequently seen in the output of a certain manufacturing process. Each item can be classified into one of the four classes AB, , , , where denotes the absence of the type-A defect. For 100 inspected items, the following frequencies were observed:AB 48, 18,
10.67 Vehicles can turn right, turn left, or continue straight ahead at a certain intersection. It is hypothesized that half the vehicles entering this intersection will continue straight ahead. Of the other half, equal proportions will turn right and left. Fifty vehicles were observed to have the
10.68 A manufacturer of stereo amplifiers has three assembly lines. We want to test the hypothesis that the three lines do not differ with respect to the number of defectives produced. Independent samples of 30 amplifiers each are selected from the output of the lines, and the number of defectives
10.69 Two inspectors are asked to rate independent samples of textiles from the same loom.Inspector A reports that 18 out of 25 samples fall in the top category, while inspector B reports that 20 out of 25 samples merit the top category. Do the inspectors appear to differ in their assessments?Use .
10.70 Two chemicals, A and B, are designed to protect pine trees from a certain disease. One hundred trees are sprayed with chemical A, and 100 are sprayed with chemical B. All trees are subjected to the disease, with the following results:Do the chemicals appear to differ in their ability to
10.71 A study of the relationship between athletic involvement and academic achievement for college students sampled randomly 852 students.The selected students were categorized according to amount of athletic involvement and gradepoint averages at graduation. The results are listed in table
10.72 Refer to Exercise 10.66. Test the hypothesis that the type A defects occur independently of the type B defects. Use .
10.73 A new sick-leave policy is being introduced into a firm. A sample of employee opinions showed the following breakdowns by sex and opinion:Does the reaction to the new policy appear to be related to sex? Test at the 5% significance level. Faver Oppose Undecided Male 31 44 6 Female 42 36 8
10.74 A sample of 150 people is observed using one of four entrances to a commercial building. The data are as follows:a Test the hypothesis that all four entrances are used equally often. Use .b Entrances 1 and 2 are on a subway level, while entrances 3 and 4 are on ground level. Test the
10.75 The use of aerosol dispensers has been somewhat controversial because of their possible effects on the ozone. A random sample of 300 women in 2003 found that 35% feared the aerosol effects on ozone, whereas only 29% of a sample of 300 stated this fear in 2007. Is there a significant
10.76 The study referenced in Exercise 10.75 was actually a 5-year study, with a random sample of 300 respondents per year. The percents of respondents stating that the aerosol dispensers did not spray properly were as follows:Are there significant differences among these percentages at the 1%
10.77 Industrial workers who are required to wear respirators were checked periodically to see that the equipment fit properly. From past records, it was expected that 1.2% of those checked would fail (i.e., their equipment would not fit property).The data from one series of checks were as
10.78 In a study of 1,000 major U.S. firms in 2001, 54%stated that quality of life was a major factor in locating corporate headquarters. A similar study of 1,000 firms in 2006 showed 55% making this statement. Is this a significant change at the 5%significance level?
10.79 For fabric coming off a certain loom, the number of defects per square yard is counted on 50 sample specimens, each 1 square yard in size. The results are as follows:Test the hypothesis that the data come from a Poisson distribution. Use 0.05. Number of Defects Frequency of Observation
10.61 Bennett et al. (Journal of Professional Issues in Engineering Education and Practice, 2002) studied conditions of existing bridges in Tennessee that were built during 1950–56 using prestressed concrete segments. They recorded number of spans, length, and average daily traffic among other
10.60 The Tennessee Board of Architectural and Engineering Examiners requested the Tennessee Society of Professional Engineers and the Consulting Engineers of Tennessee to look into various issues related to the professional registration of engineers. In response to this request, a Blue Ribbon
10.59 It is well-known that the linear systems arising from spatial discretizations of fluid mechanics problems grow rapidly as the size of the problem increases. The solution process involves the inversion of a Laplacian in each spatial direction.The larger number of iterations involved lead to
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