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Miller And Freunds Probability And Statistics For Engineers 9th Edition Richard A. Johnson - Solutions

15.20 The data of Exercise 15.19 may be looked upon as evidence that the standard of 4% defectives is being exceeded. (a) Use the data of Exercise 15.19 to construct new control limits for the fraction defective. (b) Using the limits found in part (a), continue the control of the process by
15.19 Twenty-five successive samples of 200 propellers, each taken from a production line, contained, respectively, 1, 8, 4, 6, 10, 7, 9, 5, 1, 0, 4, 8, 10, 3, 12, 5, 9, 16, 13, 7, 8, 4, 2, 9 and 2 defectives. If the fraction of defectives is to be maintained at 0.04, construct a p chart for these
15.18 Calculate x and R for the data of part (c) of Exercise 15.17 and use these values to construct the central lines and three-sigma control limits for new x and R charts to be used in the control of the heights of the shock shafts.
15.17 The specifications require that the height of shock shafts have μ = 1.6 meters and σ = 0.03 meters. (a) Use the specifications to calculate a central line and three-sigma control limits for an x chart with n = 5. (b) Use the specifications to calculate a central line and three-sigma control
15.16 Nonparametric tolerance limits can be based on the extreme values in a random sample of size n from any continuous population. The following equation relates the quantities n, P, and α, where P is the minimum proportion of the population contained between the smallest and the largest
15.14 In a study designed to determine the number of turns required for an artillery-shell fuse to arm, 80 fuses, rotated on a turntable, average 45.6 turns with a standard deviation of 5.5 turns. Establish tolerance limits for which one can assert with 95% confidence that at least 99% of the
15.13 To check the strength of carbon steel for use in chain links, the yield stress of a random sample of 25 pieces was measured, yielding a mean and a standard deviation of 52,800 psi and 4,600 psi, respectively. Establish tolerance limits with α = 0.05 and P = 0.99, and express in words what
15.12 A process for the manufacturer of 4-by-8-foot woodgrained panels has performed in the past with an average of 2.7 imperfections per 100 panels. Construct a chart to be used in the inspection of the panels and discuss the control if 25 successive 100-panel lots contained, respectively, 4, 1,
15.11 The standard for a process producing tin plate in a continuous strip is 5 defects in the form of pinholes or visual blemishes per 100 feet. Based on the following set of 25 observations, giving the number of defects per 100 feet, can it be concluded that the process is in control to this
15.10 The specifications for a certain mass-produced valve prescribe a testing procedure according to which each valve can be classified as satisfactory or unsatisfactory (defective). Past experience has shown that the process can perform so that p = 0.03. Construct a three-sigma control chart for
15.9 The data of Exercise 15.8 may be looked upon as evidence that the standard of 3% unusable bearings is being exceeded. (a) Use the data from Exercise 15.8 to construct new control limits for the fraction unusable. (b) Using the control limits found in part (a), continue the control of the
15.8 Thirty-five consecutive samples of 100 bearings each, taken from a factory, had, respectively, 1, 2, 5, 3, 4, 2, 6, 8, 1, 2, 3, 9, 8, 0, 12, 10, 5, 4, 1, 8, 6, 7, 9, 4, 8, 1, 2, 6, 7, 5, 8, 1, 3, 4 and 2 unusable bearings. If the fraction unusable is to be maintained at 0.03, construct a p
15.7 Suppose that with the samples of Exercise 15.6, it is desired to establish control also over the variability of the process. Using the method of Exercise 15.5 and the values of x and s given in Exercise 15.6, calculate the central line and the central limits for a σ chart with n = 5.
5.6 In order to establish control charts for an extraction job, 30 samples of five measurements of the extracted ores are taken, and the results are x = 25.96 tons and s = 1.5 tons. Using the method of Exercise 15.5, construct an x chart for n = 5 and on it plot the following means obtained in 25
15.5 If the sample standard deviations instead of the sample ranges are used to estimate σ, the control limits for the resulting x chart are given by x ± A1 s, where s is the mean of the sample standard deviations obtained from given data, and A1 can be found in Table 8W. Note that in connection
15.4 Reverse-current readings (in nanoamperes) are made at the location of a transistor on an integrated circuit. A sample of size 10 is taken every half hour. Since some of the units may prove to be “shorts” or “opens,” it is not always possible to obtain 10 readings. The following table
15.3 The following data give the means and ranges of 25 samples, each consisting of 4 compression test results on steel forgings, in thousands of pounds per square inch: Sample 12345678 x 45.4 48.1 46.2 45.7 41.9 49.4 52.6 54.5 R 2.7 3.1 5.0 1.6 2.2 5.7 6.5 3.6 Sample 9 10 11 12 13 14 15 16 x 45.1
15.2 Calculate x and R of the data of part (c) of Exercise 15.1, and use these values to construct the central lines and three-sigma control limits for new x and R charts to be used in the control of the thickness of the scrap steel.
15.1 A steel manufacturer extrudes scrap for manufacturing blades. Specifications require that the thickness of this scrap has μ = 0.020 mm and σ = 0.005 mm. (a) Use the specifications to calculate a central line and three-sigma control limits for an x chart with n = 10. (b) Use the
14.26 Survival times (days) of fuel rods in a nuclear reactor are as follows: 16 11 24 18 31 15 12 21 Test at the 0.01 level of significance whether these data are consistent with the assumption of a log-normal distribution of survival times. Use the KolmogorovSmirnov test and see Exercise 14.14.
14.25 With reference to Exercise 14.24, test for randomness with level 0.05.
14.24 The difference between the observed flux and the theoretical value was observed at 20 points within a reactor. The values were 2 −2 −4 −6 −3 −6 3 −526 8 5 3 9 7 32 −1 −3 −1 Use a sign test at the 0.036 level to test the null hypothesis μ = 0 versus the alternative
14.23 With reference to Example 2, Chapter 2, use the U statistic to test the null hypothesis of equality versus the alternative that the distribution of copper content from the first heat is stochastically larger than the distribution for the second heat. Following the approach in Exercise
14.22 When two populations have the same probability density function, each outcome of n1 ranks for the first sample, out of the possible values 1, 2,..., n1 +n2, is equally likely. (a) Write out all of the possible outcomes when n1 = 3 = n2. (b) Evaluate U1 at each of the outcomes and construct
14.21 The total number of vehicles crossing a toll booth each day during the month of November were: 326 246 341 148 251 296 321 196 255 751 128 506 681 186 269 345 883 543 663 429 861 189 482 683 296 199 495 330 428 196 Making use of the fact that the median is 328, test at the 0.01 level of
14.20 To test whether radio signals from deep space contain a message, an interval of time could be subdivided into a number of very short intervals and it could then be determined whether the signal strength exceeded a certain level (background noise) in each short interval. Suppose that the
14.19 The following are the data on time taken by a computer engineer to assemble 8 computers each for 3 types of mother boards. Motherboard 1: 16 12 8 15 19 10 7 15 Motherboard 2: 16 13 10 14 13 19 21 11 Motherboard 3: 7 15 9 16 14 18 15 26 Use the H test at the 0.05 level of significance to test
14.18 To find the best order of tools on a factory workbench, two different orders were compared by simulating an operational condition and measuring the response time taken to respond to the condition change. The response time (in minutes) of 16 engineers (randomly assigned to the two different
14.17 Referring to Exercise 12.6, use the U statistic at the 0.05 level of significance to test whether weight loss using lubricant A tends to be less than the loss using lubricant B.
14.16 According to Einstein’s theory of relativity, light should bend when it passes through a gravitational field. This was first tested experimentally in 1919 when photographs were taken of stars near the sun during a total eclipse and again when the sun had moved to another part of the sky.
14.15 In a vibration study, certain airplane components were subjected to severe vibrations until they showed structural failures. Given the following failure times (in minutes), test whether they can be looked upon as a sample from an exponential population with the mean μ = 10: 1.5 10.3 3.6 13.4
14.14 The P-value on page 476 was calculated using the R software command ks.test(x, "punif", 0,30, alternative = "t") The following are 15 measurements of the boiling point of a silicon compound (in degrees Celsius): 166 141 136 154 170 162 155 146 183 157 148 132 160 175 150 (a) Use the
14.13 The following are 42 consecutive pizza breads baked by a newly improved oven model during 6 weeks: 25, 28, 32, 31, 30, 29, 16, 18, 31, 24, 72, 55, 61, 33, 30, 44, 46, 59, 62, 75, 75, 80, 70, 64, 48, 52, 39, 38, 61, 64, 38, 48, 35, 34, 49, 58, 63, 36, 75, 80, 32, and 48. Use the method of runs
14.12 The following are the graded scores (out of 20) obtained by a class of 28 students in statistics: 12, 8, 6, 10, 9, 15, 18, 19, 20, 18, 20, 16, 12, 10, 14, 16, 17, 19, 20, 20, 14, 11, 12, 15, 17, 16, 12, and 17. Test for randomness at the 0.05 level of significance.
14.11 The following arrangement indicates whether 60 consecutive cars which went by the toll booth of a bridge had local plates, L, or out-of-state plates, O: LLOLLLLOOLLLLOLOOLLLLOLOOLLLLL OLLLOLOLLLLOOLOOOOLLLLOLOOLLLO Test at the 0.05 level of significance whether this arrangement of L’s and
14.10 A panel of 8 judges was asked to rate each of 3 models developed by engineering students on the likelihood that these models can be practically implemented to harness the controlled fusion energy. Their ratings (in the form of judgmental probabilities) are as follows: Model Judge X Y Z A 0.21
14.9 So-called Franklin tests were performed to determine the insulation properties of grain-oriented silicon steel specimens that were annealed in five different atmospheres with the following results: Atmosphere Test Results (amperes) 1 0.58 0.61 0.69 0.79 0.61 0.59 2 0.37 0.37 0.58 0.40 0.28
14.8 A company that processes health claims maintains three centers. Software was installed so they could monitor non-business internet usage by their employees. Initially, six employees were randomly selected from each of three service centers and the number of hours of non-business internet usage
14.7 The following are the data on the strength (in psi) of 2 kinds of adhesives: Adhesive 1: 4500 4400 4110 4450 4280 4940 4450 4610 4320 4210 4250 4280 4800 4340 4480 4450 4410 4190 4250 4800 Adhesive 2: 4100 4800 4720 4620 4610 4180 4190 4250 4360 4290 4400 4310 5080 4550 4980 4780 4860 4440
14.6 The following are the self-reported times (hours for month), spent on homework, by random samples of juniors in two different majors. Major 1: 63 72 29 58 81 65 79 57 40 76 47 55 60 Major 2: 41 32 26 43 78 49 39 56 15 54 8 66 64 Use the U test at the 0.05 level of significance to test whether
14.5 Comparing two types of automobile engines, a consumer testing service obtained the following pickup (0 – 100 kmph) times (rounded to the nearest tenth of a second): Engine A: 13.3 12.1 14 .6 8.9 9.5 12.4 13.2 13.5 13.9 12.9 Engine B: 12.6 13.1 9.8 10.4 12.5 13.6 13.0 12.2 9.9 11.5 Use the U
14.4 The following are the number of classes attended by 2 students on 20 days: 3 and 5, 1 and 2, 3 and 4, 2 and 5, 5 and 3, 4 and 2, 1 and 3, 1 and 4, 1 and 2, 2 and 4, 3 and 2, 2 and 5, 5 and 5, 1 and 3, 2 and 4, 2 and 2, 2 and 3, 3 and 5, 3 and 3, 2 and 1. Use the sign test at the 0.01 level of
14.3 With reference to Exercise 2.12, which pertained to the particle size of cement dust in a factory producing cement, use the sign test at the 0.05 level of significance to test the null hypothesis μ = 15.13 hundredth of a micron against the alternative hypothesis μ < 15.13 hundredth of a
14.2 The time sheet of a factory showed the following sample data (in hours) on the time spent by a worker operating a hydraulic gear lift: 1.0, 0.8, 0.5, 0.9, 1.2, 0.9, 1.4, 10, 1.3, 0.8, 1.5, 1.2, 1.9, 1.1, 0.7, 0.8, 1.1, 1.2, 1.5, 1.1, 1.8, 0.5, 0.8, 0.9, and 1.6. Use the sign test at the 0.05
14.1 In a factory, 20 observations of the factors that could heat up a conveyor belt yielded the following results: 0.36, 0.41, 0.25, 0.34, 0.28, 0.26, 0.39, 0.28, 0.40, 0.26, 0.35, 0.38, 0.29, 0.42, 0.37, 0.37, 0.39, 0.32, 0.29 and 0.36. Use the sign test at the 0.01 level of significance to test
13.35 Refer to Exercise 13.10 where the response is y = increase in particle size. Besides the first replicate, the investigators also performed the experiments that form the star part of the design.x1 x2 y −1 0 116.0 +1 0 138.0 0 −1 78.0 0 +1 118.0 0 0 97.0 Using all 9 measurements, fit a
13.34 With reference to the Example 3 concerning improvements in the safety of an ignitor, the time to reach maximum pressure was also recorded. Two replicates were run of the factorial design and the times to reach maximum pressure recorded. Analyze the results of this experiment.Time
13.33 With reference to the example of the 23 design on page ***, express the total sum of squares as the sum of the contributions from each of the seven treatments plus the error sum of squares. This decomposition is the basis for the analysis variance and it is summarized in the first column of
13.32 The total sum of squares is given by k i=1 r j=1(yi j − y) 2 where the overall mean y = k i=1 r j=1(yi j/n). With reference to Exercise 13.27, show that the total sum of squares can be expressed as the sum of squares due to each of the treatment SSA, SSB, and SSAB plus the error of the
13.31 Given the following results from a 23 factorial experiment, Factor A Factor B Factor C Rep. 1 Rep. 2 −1 −1 −1 13.8 14.6 1 −1 −1 10.8 8.4 −1 1 −1 9.0 9.8 1 1 −1 10.1 10.9 −1 −1 1 14.4 13.6 1 −1 16.2 8.6 −1 1 17.7 7.9 1 1 19.0 8.2 summarize the experiment according to
13.30 A computer engineer studied the working of a motherboard under different conditions. The response is heating effect (coded units). The factors are fan connectors (no. of pins), power connection (type), and chipsets (direction). Factor A Factor B Factor C Rep. 1 Rep. 2 −1 −1 −1 24.8 26.4
13.29 Trouble was being experienced by a new high-tech machine for joining two pieces of sheet metal. The two factors considered first are the pressure (low/high) and temperature of the pump low/high. The response is the diameter (mm) of a button-shaped joint which is an indirect measure of
13.28 With reference to the example on page 443, suppose a third replicate Temperature pH Rep. 3 300 2 9 350 2 23 300 3 13 350 3 25 is run. Analyze the experiment, using all 3 replicates, according to the visual procedure given in Section 13.3. Interpret the effects based on the confidence
13.27 Given the following observations, Factor P Factor Q Rep. 1 Rep. 2 −1 1 18 12 −1 −1 814 1 1 10 16 1 −1 610 Summarize the experiment according to the visual procedure given in Section 13.3. Interpret the effects based on the confidence intervals.
13.26 Given the two replicates of a 2 × 3 factorial experiment, calculate the analysis of variance tables using the formulas on page 428. Factor A Factor B Rep. 1 Rep. 2 1 1 29 35 1 2 15 17 1 3 14 22 2 1 15 13 2 2 27 25 2 3 16 24
13.25 An experiment was conducted to determine the effects of certain alloying elements on the ductility of a metal, and the following results were obtained: Breaking Strength (ft-lb) Nickel Carbon Manganese Rep. 1 Rep. 2 Rep. 3 0.0% 0.3% 0.5% 36.7 39.6 38.2 0.0 0.3 1.0 47.5 43.5 45.9 0.0 0.6 0.5
13.24 A study was conducted to measure the effect of 3 different meat tenderizers on the weight loss of steaks having the same initial (precooked) weights. The effects of cooking temperatures and cooking times also were measured by performing a 3 × 2 × 2 factorial experiment in 3 replicates. The
13.23 A footwear manufacturing machine manufactures each piece separately. Suppose pairs are manufactured, with the following results obtained for the range (number). Rubber 1 Rubber 2 Rubber 3 Rubber 4 Left foot Sole 1 Sole 2 262 279 236 248 384 349 321 363 Rubber 1 Rubber 2 Rubber 3 Rubber 4
13.22 Is there a region within the experimental region where estimated adhesion is greater than 45 grams? Construct a contour plot to show this region. Note that MINITAB does keep nonsignificant terms. Refer to Exercise 13.21.
change the response to adhesion.
13.21 Refer to Exercise 13.20. In Example 4, the experimenters also obtained the nine responses for adhesion. The business wants adhesion greater than 45 grams. Adhesion 10 48 41 40 39 44 24 31 44 Repeat the analysis in Example 4 but
13.20 MINITAB response surface analysis We illustrate the commands for the coating data in Example 4 where yield is the response. Start with the Run, Additive, Temperature, Yield in C1–C4.Dialog box: Stat> DOE > Response Surface. Click Define Custom Response . . . Type Additive and
13.19 Refer to the Example 4. Use calculus to obtain the location of the estimated maximum yield when all terms are included in the model.
13.18 The response variable Yi j in a 22 design can also be expressed as a regression model Yi j = μ + β1 x1 + β2 x2 + β12 x1 x2 + εi j where the εi j are independent normal random variables and each has mean 0 and variance σ2. Because β1 is a regression coefficient, it quantifies the
13.17 Two machines X and Y were used to produce two types of plastic polymers, PPET and PAMI. The polymers were produced using materials BA and PP. The production was run 3 times. The y values given below are the logarithms of the quantity of polymers produced. Polymer Machine Material Run. 1 Run.
13.16 The effect on engine wear of oil viscosity, temperature, and a special additive was tested using a 23 factorial design. Given the following results from the experiment, Factor A Factor B Factor C Viscosity Temperature Additive Rep. 1 Rep. 2 −1 −1 −1 3.7 4.1 1 −1 −1 4.6 5.0 −1 1
13.15 An engineering student wanted to know which factors influence the time (in seconds) for his car to go from 0 to 30 to 0 miles per hour. Factor A was the launch, which was either no wheel spin or dropping the clutch at 2,500 rpm. Factor B is either stopping with transmission in neutral or in
13.14 Tomatoes have one of highest production volumes in the world and drying is one major process for preservation. Color is an important quality index for consumers. Three factors of storage, each at two levels, are considered in a replicated 23 design. Factor Low level High level A: Storage
13.13 Two factors are thought to influence the deposition rate (seconds) for a pulse laser to deposit one monolayer of material. Initially, a 22 design was run with two factors: spot size 50 mm or 60 mm and laser energy 1.5 J/cm2 or 2.0 J/cm2. Spot Size Laser Energy Rep. 1 Rep. 2 −1 −1 8.34
13.12 Given the following observations Factor A Factor B Rep. 1 Rep. 2 1 1 20 16 1 −1 12 16 1 1 15 17 1 −1 18 12 (a) Attach the sample means at the corner of a square. Comment on any obvious pattern. (b) Obtain the point estimates of the effects and 99% confidence intervals.
13.11 Shape memory alloys can undergo a reversible phase transformation. These materials display dramatic shape memory temperature-induced deformations that are recoverable. Investigators want to evaluate the influence of two factors Factor A: Temperature at levels 350 ◦C and 450◦C Factor B:
13.10 As a preliminary step in optimizing the coating process of iron oxide nanoparticles engineers explored the effects, of two factors each having two levels on the response y = increase in particle size (%). Factor Low level High Level Factor A molecular weight of chitosan low high Factor B
13.9 Solve the 4 equations on page 426 for μ, α1,β1, and ( αβ )11 in terms of the population means μijl corresponding to the 4 experimental conditions in the first replicate. Note that these equations serve as a guide for estimating the parameters in terms of the sample means corresponding to
13.8 A market test was performed to evaluate the impact of shelf position, and label color of a canned food product on sales.Sales (dollars) Shelf Label Position Color Day 1 Day 2 Day 3 Low Red 70.10 68.00 69.50 Low Red 72.25 71.90 74.70 Low Red 78.05 74.85 82.60 Low Red 61.50 62.10 59.15 Low Green
13.7 The commercial value of softwood species would be increased if the wood could be treated to meet preserver’s standards. The response, y, is the amount of retention (lb/ft3) of the preservative. Two treatments (preservatives) were considered and the samples were either incised or unincised.
13.6 An experiment was conducted to study the effects of temperature (◦C) and quantity (g) on the solubility of a chemical in the laboratory. Temperature Quantity Situation 1 Situation 2 44 50 12 14 44 75 13 11 44 100 15 18 50 50 14 13 50 75 13 12 50 100 17 19 65 50 16 15 65 75 14 12 65 100 20 20
13.5 Suppose that in the experiment described in Example 7, Chapter 12, it is desired to determine also whether there is an interaction between the detergents and the engines; that is, whether one detergent might perform better in Engine 1, another might perform better in Engine 2, and so on.
13.4 A spoilage-retarding ingredient is added in brewing beer. To determine the extent to which the taste of the beer is affected by the amount of this ingredient added to each batch, and how such taste changes might depend on the age of the beer, a 3 × 4 factorial experiment in two replications
13.3 To determine optimum condition for a circuit board, the effects of bond strength of FR-4 (an insulating substrate) and thickness of copper lamination on the current flow are studied in a 2 × 5 factorial experiment. The results of three replicates are as follows:Bond Strength Thickness of
13.2 MINITAB can create the analysis of variance table for Example 1 concerning recycled road materials. The three levels of A are coded 1, 2, and 3, and the two levels of B are coded 1 and 2. The third column contains the values of the resiliency modulus. 1 1 707 1 1 632 1 1 604 1 2 652 … Dialog
13.1 Given the two replications of a 2 × 3 factorial experiment, calculate the analysis of variance table using the formulas on pages *** and ***. Factor A Factor B Rep. 1 Rep. 2 1 1 15 21 1 2 13 1 310 8 2 1 11 2 2 16 14 2 3 513
12.54 Benjamin Franklin (1706–1790) conducted an experiment to study the effect of water depth on the amount of drag on a boat being pulled up a canal. He made a 14-foot trough and a model boat 6 inches long. A thread was attached to the bow, put through a pulley, and then a weight was attached.
12.53 Using the alternative calculation formula verify analysis of variance table for the paper-strength in Example 4.
#!# 12.52 Three different instrument panel configurations were tested by placing airline pilots in flight simulators and testing their reaction time to simulated flight emergencies. Eight pilots were assigned to each instrument panel configuration. Each pilot was faced with 10 emergency
12.51 Refer to Exercise 12.50. (a) Perform an analysis of covariance. Test for a difference in treatments using level of significance 0.05. (b) Compare your analysis in part (a) with the analysis of variance. Is the covariate important?
12.50 The state highway department does an experiment to compare three types of surfacing treatments and the response y is road roughness. The following table also gives average daily traffic volume x. Suppose the data are, in suitable units,Treatment 1 x y 5 12 5 10 2 5 Treatment 2 x y 3 3 2 2 1 1
12.49 An experiment is conducted with k = 5 treatments, one covariate x, and n = 6. Calculations result in the sums of squares error SSEx = 14.4, SSEtr. = 4.69, and SSEtr,x = 1.21. Assuming that the analysis of covariance model is reasonable, conduct the F-test for treatment differences and the
12.48 Using q0.05 = 4.041 for the Tukey HSD method, compare the pollution levels of the three agencies in Exercise 12.47.
12.47 Samples of groundwater were taken from 5 different toxic-waste dump sites by each of 3 different agencies: the EPA, the company that owned each site, and an independent consulting engineer. Each sample was analyzed for the presence of a certain contaminant by whatever laboratory method was
12.46 Using q0.05 = 4.339 for the Tukey HSD method, compare the treatments in Exercise 12.45.
12.45 Given the following data from a randomized block design,Blocks 1 234 Treatment 1 9 10 2 7 Treatment 2 6 13 1 12 Treatment 3 9 16 9 14 (a) Decompose each observation yi j as yi j = y• • + ( yi• − y• • ) + ( y• j − y• • ) + ( yi j − yi• − y• j + y• • ) (b) Obtain
12.44 Refer to Example 11. Ignore the covariate original reflectivity. Perform an analysis of variance take α = 0.05
12.43 To determine the effect of height on power generated in a hydroelectric power plant, the following observations were made:Total height Power generated (m) (megawatts per turbine) 250 13.25 14.00 13.00 13.75 14.00 300 14.25 13.75 15.00 14.00 14.25 350 15.75 16.00 14.25 15.00 15.00 400 14.50
12.42 Assume the following data obey the one-way analysis of variance model. Treatment I: 8 9 12 7 Treatment II:54 8481 Treatment III:35 001 (a) Decompose each observation yi j as yi j = y + ( yi − y ) + ( yi j − yi ) (b) Obtain the sums of squares and degrees of freedom for each array. (c)
12.41 Use computer software to work Exercise 12.37. Do’s and Don’ts Do’s 1. Whenever possible, randomize the assignment of treatments in the completely randomized design. In other designs, randomize the assignments of treatment within the restraints of the design. 2. When numerous
12.40 To compare power consumption by a newly developed low-power USB device under three test run conditions and record the data transmission rate at the same time, a computer engineer obtained the following results, where the power consumption, x, is in Watts, and the data transmission rate, y, is
12.39 Four different railroad-track cross-section configurations were tested to determine which is most resistant to breakage under use conditions. Ten miles of each kind of track were laid in each of 5 locations, and the number of cracks and other fracture-related conditions (y) was measured over
12.38 MINITAB calculation of balanced analysis of covariance We illustrate the MINTAB commands for Example 11 concerning surface reflectivity. Data: C1(Tr) : 1 1 1 1 2 2 2 2 3 3 3 3 C2(x): 0.90 0.95 1.05 0.80 0.50 0.40 0.15 0.25 0.20 0.55 0.30 0.40 C3(y): 1.05 0.95 1.15 0.85 1.10 1.00 0.90 0.80
12.37 An experimenter wants to compare the time to failure y after rebuilding a robotic welder by three different methods but adjusting for the covariate x = age of robotic welder. Suppose the data, in thousands of hours, are Method 1 x y 7 2 11 5 6 2 Method 2 x y 6 4 8 5 4 3 Method 3 x y 5 6 3 5 4
12.36 The Bonferroni inequality states that P ( ∩i Ci ) ≥ 1 − i P (Ci ) (a) Show that this holds for 3 events. (b) Let Ci be the event that the ith confidence interval will cover the true value of the parameter for i = 1,..., m. If P(Ci) ≤ α/m, so the probability of not covering the

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