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applied statistics and probability for engineers

Probability And Statistics For Engineering And The Sciences 7th Edition Dave Ellis, Jay L Devore - Solutions

46. In Example 10.10, subtract x i from each observation in the ith sample (i 1, . . . , 6) to obtain a set of 18 residuals.Then construct a normal probability plot and comment on the plausibility of the normality assumption.
44. Four types of mortars—ordinary cement mortar (OCM), polymer impregnated mortar (PIM), resin mortar (RM), and polymer cement mortar (PCM)—were subjected to a compression test to measure strength (MPa). Three strength observations for each mortar type are given in the article.“Polymer
43. Let c1, c2, . . . , cI be numbers satisfying ci 0. Thenci i c11 cII is called a contrast in the is.Notice that with c1 1, c2 1, c3 cI 0,ci i 1 2, which implies that every pairwise difference between is is a contrast (so is, e.g., 1 .52 .53). A method attributed to
42. The critical flicker frequency (cff) is the highest frequency(in cycles/sec) at which a person can detect the flicker in a ?
41. Four laboratories (1–4) are randomly selected from a large population, and each is asked to make three determinations of the percentage of methyl alcohol in specimens of a compound taken from a single batch. Based on the accompanying data, are differences among laboratories a source of
40. Refer to Exercise 38. What is for the test when true average DNA content is identical for three of the diets and falls below this common value by 1 standard deviation () for the other two diets?
39. Referring to Exercise 38, construct a t CI for 1 (2 3 4 5)/4 which measures the difference between the average DNA content for the starch diet and the combined average for the four other diets. Does the resulting interval include zero?
38. An article in the British scientific journal Nature (“Sucrose Induction of Hepatic Hyperplasia in the Rat,” August 25, 1972: 461) reports on an experiment in which each of five groups consisting of six rats was put on a diet with a different carbohydrate. At the conclusion of the
37. Numerous factors contribute to the smooth running of an electric motor (“Increasing Market Share Through Improved Product and Process Design: An Experimental Approach,”Quality Engineering, 1991: 361–369). In particular, it is desirable to keep motor noise and vibration to a minimum.To
36. The article “Computer-Assisted Instruction Augmented with Planned Teacher/Student Contacts” (J. Exp. Educ., Winter, 1980–1981: 120–126) compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion (L/D), programmed
34. Simplify E(MSTr) for the random effects model when J1 J2 JI J.
33. Suppose that Xij is a binomial variable with parameters n and pi (so approximately normal when npi 5 and nqi 5).Then since i npi, V(Xij) 2 i npi(1 pi) i(1 i /n). How should the Xijs be transformed so as to stabilize the variance? [Hint: g(i) i(1 i /n).]
32. In an experiment to compare the quality of four different brands of reel-to-reel recording tape, five 2400-ft reels of each brand (A–D) were selected and the number of flaws in each reel was determined.A: 10 5 12 14 8 B: 14 12 17 9 8 C: 13 18 10 15 18 D: 17 16 12 22 14 It is believed that the
31. When sample sizes are not equal, the noncentrality parameter is Ji2 i /2 and 2 (1/I)Ji2 i /2. Referring to Exercise 22, what is the power of the test when 2 3, 1 2 , and 4 2 ?
29. When sample sizes are equal (Ji J), the parameters1, 2, . . . , I of the alternative parameterization are restricted by i 0. For unequal sample sizes, the most natural restriction is Jii 0. Use this to show that E(MSTr) 2 Ji2 iWhat is E(MSTr) when H0 is true? [This expectation
28. For a single-factor ANOVA with sample sizes Ji (i 1, 2, . . . , I), show that SSTr Ji(Xi X)2 iJiX2 i nX 2, where n Ji.
27. Although tea is the world’s most widely consumed beverage after water, little is known about its nutritional value. Folacin is the only B vitamin present in any significant amount in tea, and recent advances in assay methods have made accurate determination of folacin content feasible.
26. Samples of six different brands of diet/imitation margarine were analyzed to determine the level of physiologically active polyunsaturated fatty acids (PAPFUA, in percentages), resulting in the following data:
24. The following partial ANOVA table is taken from the article“Perception of Spatial Incongruity” (J. Nervous and Mental Disease, 1961: 222) in which the abilities of three different groups to identify a perceptual incongruity were assessed and compared. All individuals in the experiment had
23. Apply the modified Tukey’s method to the data in Exercise 22 to identify significant differences among the is.
22. The following data refers to yield of tomatoes (kg/plot) for four different levels of salinity; salinity level here refers to electrical conductivity (EC), where the chosen levels were EC 1.6, 3.8, 6.0, and 10.2 nmhos/cm:1.6 59.5 53.3 56.8 63.1 58.7 3.8 55.2 59.1 52.8 54.5 6.0 51.7 48.8 53.9
21. The article “The Effect of Enzyme Inducing Agents on the Survival Times of Rats Exposed to Lethal Levels of Nitrogen Dioxide” (Toxicology and Applied Pharmacology, 1978: 169–174) reports the following data on survival times for rats exposed to nitrogen dioxide (70 ppm) via different
20. Refer to Exercise 19 and suppose x1 10, x2 15, and x3 20. Can you now find a value of SSE that produces such a contradiction between the F test and Tukey’s procedure?
18. Consider the accompanying data on plant growth after the application of different types of growth hormone.1 13 17 7 14 2 21 13 20 17 Hormone 3 18 15 20 17 4 7 11 18 10 5 6 11 15 8a. Perform an F test at level .05.b. What happens when Tukey’s procedure is applied?
17. Refer to Exercise 5. Compute a 95% t CI for 1 2 (1 2) 3.
16. Reconsider the axial stiffness data given in Exercise 8.ANOVA output from MINITAB follows:Analysis of Variance for stiffness Source DF SS MS F P length 4 43993 10998 10.48 0.000 Error 30 31475 1049 Total 34 75468 Level N Mean StDev 4 7 333.21 36.59 6 7 368.06 28.57 8 7 375.13 20.83 10 7 407.36
15. Use Tukey’s procedure on the data of Exercise 6 to identify differences in true average total Fe among the four types of formations (use MSE 15.64).
14. Use Tukey’s procedure on the data in Exercise 4 to identify differences in true average flight times among the four types of mosquitos.
13. Repeat Exercise 12 supposing that x 2 502.8 in addition to x3 427.5.
12. In Exercise 11, suppose x 3 427.5. Now which true average spreading rates differ significantly from one another?Be sure to use the method of underscoring to illustrate your conclusions, and write a paragraph summarizing your results.
10. In single-factor ANOVA with I treatments and J observations per treatment, let (1/I)i.a. Express E(X) in terms of . [Hint: X (1/I)Xi]b. Compute E(X2 i). [Hint: For any rv Y, E(Y2) V(Y)[E(Y)]2.]c. Compute E(X2).d. Compute E(SSTr) and then show that?
9. Six samples of each of four types of cereal grain grown in a certain region were analyzed to determine thiamin content, resulting in the following data (g/g):Wheat 5.2 4.5 6.0 6.1 6.7 5.8 Barley 6.5 8.0 6.1 7.5 5.9 5.6 Maize 5.8 4.7 6.4 4.9 6.0 5.2 Oats 8.3 6.1 7.8 7.0 5.5 7.2 Does this data
8. A study of the properties of metal plate-connected trusses used for roof support (“Modeling Joints Made with Light-Gauge Metal Connector Plates,” Forest Products J., 1979: 39–44)yielded the following observations on axial stiffness index(kips/in.) for plate lengths 4, 6, 8, 10, and 12 in?
7. In an experiment to investigate the performance of four different brands of spark plugs intended for use on a 125-cc two-stroke motorcycle, five plugs of each brand were tested and the number of miles (at a constant speed) until failure was observed. The partial ANOVA table for the data is given
6. The article “Origin of Precambrian Iron Formations” (Econ.Geology, 1964: 1025–1057) reports the following data on total Fe for four types of iron formation (1 carbonate, 2 silicate, 3 magnetite, 4 hematite).1: 20.5 28.1 27.8 27.0 28.0 25.2 25.3 27.1 20.5 31.3 2: 26.3 24.0 26.2 20.2
4. In a study to assess the effects of malaria infection on mosquito hosts (“Plasmodium Cynomolgi: Effects of Malaria Infection on Laboratory Flight Performance of Anopheles Stephensi Mosquitos,” Experimental Parasitology, 1977:397–404), mosquitos were fed on either infective or noninfective
3. The lumen output was determined for each of I 3 different brands of 60-watt soft-white lightbulbs, with J 8 bulbs of each brand tested. The sums of squares were computed as SSE 4773.3 and SSTr 591.2. State the hypotheses of interest (including word definitions of parameters), and use the
2 were computed as MSTr 2673.3 and MSE 1094.2, respectivelya. Use the F test at level .05 to test H0: 1 2 3 4 5 versus Ha: at least two is are unequal.b. What can be said about the P-value for the test?2. Suppose that the compression strength observations on the fourth type of box in
1. In an experiment to compare the tensile strengths of I 5 different types of copper wire, J 4 samples of each type were used. The between-samples and within-samples estimates of
Referring to Exercise 92, develop a large-sample confidence interval formula for 1 2. Calculate the interval for the data given there using a confidence level of 95%.
Let X1, . . . , Xm be a random sample from a Poisson distribution with parameter 1, and let Y1, . . . , Yn be a random sample from another Poisson distribution with parameter 2.We wish to test H0: 1 2 0 against one of the three standard alternatives. Since for a Poisson distribution,
Then X1 is the number of pairs in which both treatments were successful, and similarly for X2, X3, and X4. The test statistic for testing equal efficacy of the two treatments is given by (X2 X3)/(X2 X3), which has approximately a standard normal distribution when H0 is true. Use this to test
McNemar’s test, developed in Exercise 54, can also be used when individuals are paired (matched) to yield n pairs and then one member of each pair is given treatment 1 and the other is given treatment
The following data refers to airborne bacteria count (number of colonies/ft3) both for m 8 carpeted hospital rooms and for n 8 uncarpeted rooms (“Microbial Air Sampling in a Carpeted Hospital,” J. Environmental Health, 1968:405). Does there appear to be a difference in true average bacteria
Suppose a level .05 test of H0: 1 2 0 versus Ha:1 2 0 is to be performed, assuming 1 2 10 and normality of both distributions, using equal sample sizes?
The paper “Quantitative Assessment of Glenohumeral Translation in Baseball Players” (The Amer. J. of Sports Med., 2004: 1711–1715) considered various aspects of shoulder motion for a sample of pitchers and another sample of position players (“glenohumeral” refers to the articulation
Wait staff at restaurants have employed various strategies to increase tips. An article in the Sept. 5, 2005 The New Yorker reported that “In one study a waitress received 50% more in tips when she introduced herself by name than when she didn’t.” Consider the following (fictitious) data on
An experiment to determine the effects of temperature on the survival of insect eggs was described in the article“Development Rates and a Temperature-Dependent Model of Pales Weevil” (Environ. Entomology, 1987: 956–962).At 11°C, 73 of 91 eggs survived to the next stage of development. At
How does energy intake compare to energy expenditure?One aspect of this issue was considered in the article“Measurement of Total Energy Expenditure by the Doubly Labelled Water Method in Professional Soccer Players” (J.of Sports Sciences, 2002: 391–397), which contained the accompanying data
Acrylic bone cement is commonly used in total joint arthroplasty as a grout that allows for the smooth transfer of loads from a metal prosthesis to bone structure. The paper“Validation of the Small-Punch Test as a Technique for Characterizing the Mechanical Properties of Acrylic Bone Cement”
The accompanying data on response time appeared in the article “The Extinguishment of Fires Using Low-Flow Water Hose Streams—Part II” (Fire Technology, 1991: 291–320).Good visibility.43 1.17 .37 .47 .68 .58 .50 2.75 Poor visibility 1.47 .80 1.58 1.53 4.33 4.23 3.25 3.22 The authors
The accompanying summary data on the ratio of strength to cross-sectional area for knee extensors is taken from the article “Knee Extensor and Knee Flexor Strength: CrossSectional Area Ratios in Young and Elderly Men” (J. of Gerontology, 1992: M204–M210).Sample Sample Standard Group Size Mean
Long-term exposure of textile workers to cotton dust released during processing can result in substantial health problems, so textile researchers have been investigating methods that will result in reduced risks while preserving important fabric properties. The accompanying data on roving cohesion
The article “Pine Needles as Sensors of Atmospheric Pollution” (Environ. Monitoring, 1982: 273–286) reported on the use of neutron-activity analysis to determine pollutant concentration in pine needles. According to the article’s authors,“These observations strongly indicated that for
The article “Two Parameters Limiting the Sensitivity of Laboratory Tests of Condoms as Viral Barriers” (J. of Testing and Eval., 1996: 279–286) reported that, in brand A condoms, among 16 tears produced by a puncturing needle, the sample mean tear length was 74.0 m, whereas for the 14 brand B
The derailment of a freight train due to the catastrophic failure of a traction motor armature bearing provided the impetus for a study reported in the article “Locomotive Traction Motor Armature Bearing Life Study” (Lubrication Engr., Aug. 1997: 12–19). A sample of 17 high-mileage traction
The following summary data on bending strength (lb-in/in)of joints is taken from the article “Bending Strength of Corner Joints Constructed with Injection Molded Splines”(Forest Products J., April, 1997: 89–92).Sample Sample Sample Type Size Mean SD Without side coating 10 80.95 9.59 With
The article “Quantitative MRI and Electrophysiology of Preoperative Carpal Tunnel Syndrome in a Female Population” (Ergonomics, 1997: 642–649) reported that(473.3, 1691.9) was a large-sample 95% confidence interval for the difference between true average thenar muscle volume (mm3) for
The accompanying data was obtained in a study to evaluate the liquefaction potential at a proposed nuclear power station (“Cyclic Strengths Compared for Two Sampling Techniques,” J. Geotechnical Division, Am. Soc. Civil Engrs.Proceedings, 1981: 563–576). Before cyclic strength testing, soil
Is the response rate for questionnaires affected by including some sort of incentive to respond along with the questionnaire? In one experiment, 110 questionnaires with no incentive resulted in 75 being returned, whereas 98 questionnaires that included a chance to win a lottery yielded 66
The authors of the article “Dynamics of Canopy Structure and Light Interception in Pinus elliotti, North Florida”(Ecological Monographs, 1991: 33–51) planned an experiment to determine the effect of fertilizer on a measure of leaf area. A number of plots were available for the study, and half
The accompanying summary data on compression strength(lb) for 12 10 8 in. boxes appeared in the article“Compression of Single-Wall Corrugated Shipping Containers Using Fixed and Floating Test Platens” (J. Testing and Evaluation, 1992: 318–320). The authors stated that “the difference
The article “Enhancement of Compressive Properties of Failed Concrete Cylinders with Polymer Impregnation”(J. Testing and Evaluation, 1977: 333–337) reports the following data on impregnated compressive modulus (psi 106) when two different polymers were used to repair cracks in failed
In a study of copper deficiency in cattle, the copper values(g Cu/100 mL blood) were determined both for cattle grazing in an area known to have well-defined molybdenum anomalies (metal values in excess of the normal range of regional variation) and for cattle grazing in a nonanomalous area (“An
Toxaphene is an insecticide that has been identified as a pollutant in the Great Lakes ecosystem. To investigate the effect of toxaphene exposure on animals, groups of rats were given toxaphene in their diet. The article “Reproduction Study of
Refer to Example 9.7. Does the data suggest that the standard deviation of the strength distribution for fused specimens is smaller than that for not-fused specimens? Carry out a test at significance level .01 by obtaining as much information as you can about the P-value.
Return to the data on maximum lean angle given in Exercise 28 of this chapter. Carry out a test at significance level .10 to see whether the population standard deviations for the two age groups are different (normal probability plots support the necessary normality assumption).
Give as much information as you can about the P-value of the F test in each of the following situations:a. 1 5, 2 10, upper-tailed test, f 4.75b. 1 5, 2 10, upper-tailed test, f 2.00c. 1 5, 2 10, two-tailed test, f 5.64d. 1 5, 2 10, lower-tailed test, f .200e. 1 35, 2
Obtain or compute the following quantities:a. F.05,5,8b. F.05,8,5c. F.95,5,8d. F.95,8,5e. The 99th percentile of the F distribution with 1 10, 2 12f. The 1st percentile of the F distribution with 1 10, 2 12 g. P(F 6.16) for 1 6, 2 4 h. P(.177 F 4.74) for 1 10, 2 5
Two different types of alloy, A and B, have been used to manufacture experimental specimens of a small tension link to be used in a certain engineering application. The ultimate strength (ksi) of each specimen was determined, and the results are summarized in the accompanying frequency
In medical investigations, the ratio p1/p2 is often of more interest than the difference p1 p2 (e.g., individuals given treatment 1 are how many times as likely to recover as those given treatment 2?). Let ˆ pˆ1/pˆ2. When m and n are both large, the statistic ln( ˆ) has approximately a
Ionizing radiation is being given increasing attention as a method for preserving horticultural products. The article “The Influence of Gamma-Irradiation on the Storage Life of Red Variety Garlic” (J. of Food Processing and Preservation, 1983: 179–183) reports that 153 of 180 irradiated
It is thought that the front cover and the nature of the first question on mail surveys influence the response rate. The article “The Impact of Cover Design and First Questions on Response Rates for a Mail Survey of Skydivers” (Leisure
A sample of 300 urban adult residents of a particular state revealed 63 who favored increasing the highway speed limit from 55 to 65 mph, whereas a sample of 180 rural residents yielded 75 who favored the increase. Does this data indicate that the sentiment for increasing the speed limit is
Is someone who switches brands because of a financial inducement less likely to remain loyal than someone who switches without inducement? Let p1 and p2 denote the true proportions of switchers to a certain brand with and without inducement, respectively, who subsequently make a repeat purchase.
Example 7.11 gave data on the modulus of elasticity obtained 1 minute after loading in a certain configuration. The cited article also gave the values of modulus of elasticity obtained 4 weeks after loading for the same lumber specimens. The data is presented here.Observation 1 min 4 weeks
Cushing’s disease is characterized by muscular weakness due to adrenal or pituitary dysfunction. To provide effective treatment, it is important to detect childhood Cushing’s disease as early as possible. Age at onset of symptoms and age at diagnosis for 15 children suffering from the disease
In an experiment designed to study the effects of illumination level on task performance (“Performance of Complex Tasks Under Different Levels of Illumination,” J. Illuminating Eng., 1976: 235–242), subjects were required to insert a fine-tipped probe into the eyeholes of ten needles in rapid
Lactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk production. The paper“Bone Mass Is Recovered from Lactation to Postweaning in Adolescent Mothers with Low Calcium Intakes” (Amer. J.Clinical Nutr., 2004: 1322–1326) gave the following data on
Concrete specimens with varying height-to-diameter ratios cut from various positions on the original cylinder were obtained both from a normal-strength concrete mix and from a high-strength mix. The peak stress (MPa) was determined for each mix, resulting in the following data (“Effect of Length
Hexavalent chromium has been identified as an inhalation carcinogen and an air toxin of concern in a number of different locales. The article “Airborne Hexavalent Chromium in Southwestern Ontario” (J. of Air and Waste Mgmnt. Assoc., 1997: 905–910) gave the accompanying data on both indoor and
Consider the accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded condition and an abraded condition (“The Effect of Wet Abrasive Wear on the Tensile Properties of Cotton and Polyester-Cotton Fabrics,” J. Testing and Evaluation, 1993: 84–93). Use the
Refer to Exercise 34. Describe the pooled t test for testing H0: 1 2 0 when both population distributions are normal with 1 2. Then use this test procedure to test the hypotheses suggested in Exercise 33.
Consider the pooled t variable T which has a t distribution with m n 2 df when both population distributions are normal with 1 2 (see the Pooled t Procedures subsection for a description of Sp).a. Use this t variable to obtain a pooled t confidence interval formula for 1 2.b. A sample of
The article “The Effects of a Low-Fat, Plant-Based Dietary Intervention on Body Weight, Metabolism, and Insulin Sensitivity in Postmenopausal Women” (Amer. J. of Med., 2005: 991–997) reported on the results of an experiment in which half of the individuals in a group of 64 postmenopausal
The article cited in Exercise 34 in Section 7.3 gave the following summary data on proportional stress limits for specimens constructed using two different types of wood:Type Sample Sample Sample of Wood Size Mean SD Red oak 14 8.48 .79 Douglas fir 10 6.65 1.28 Assuming that both samples were
Refer to Exercise 33 in Section 7.3. The cited article also gave the following observations on degree of polymerization for specimens having viscosity times concentration in a higher range:429 430 430 431 436 437 440 441 445 446 447a. Construct a comparative boxplot for the two samples, and comment
The article “Flexure of Concrete Beams Reinforced with Advanced Composite Orthogrids” (J. of Aerospace Engr., 1997: 7–15) gave the accompanying data on ultimate load(kN) for two different types of beams.Sample Sample Sample Type Size Mean SD Fiberglass grid 26 33.4 2.2 Commercial 26 42.8 4.3
The article “Effect of Internal Gas Pressure on the Compression Strength of Beverage Cans and Plastic Bottles”(J. Testing and Evaluation, 1993: 129–131) includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another
As the population ages, there is increasing concern about accident-related injuries to the elderly. The article “Age and Gender Differences in Single-Step Recovery from a Forward Fall” (J. of Gerontology, 1999: M44–M50) reported on an experiment in which the maximum lean angle—the furthest
Tennis elbow is thought to be aggravated by the impact experienced when hitting the ball. The article “Forces on the Hand in the Tennis One-Handed Backhand” (Intl. J. of Sport Biomechanics, 1991: 282–292) reported the force (N) on the hand just after impact on a one-handed backhand drive for
The article “The Influence of Corrosion Inhibitor and Surface Abrasion on the Failure of Aluminum-Wired Twist-on Connections” (IEEE Trans. on Components, Hybrids, and Manuf. Tech., 1984: 20–25) reported data on potential drop measurements for one sample of connectors wired with alloy aluminum
Low-back pain (LBP) is a serious health problem in many industrial settings. The article “Isodynamic Evaluation of Trunk Muscles and Low-Back Pain Among Workers in a Steel Factory” (Ergonomics, 1995: 2107–2117) reported the accompanying summary data on lateral range of motion(degrees) for a
Damage to grapes from bird predation is a serious problem for grape growers. The article “Experimental Method to
Fusible interlinings are being used with increasing frequency to support outer fabrics and improve the shape and drape of various pieces of clothing. The article “Compatibility of Outer and Fusible Interlining Fabrics in Tailored Garments”(Textile Res. J., 1997: 137–142) gave the accompanying
The slant shear test is widely accepted for evaluating the bond of resinous repair materials to concrete; it utilizes cylinder specimens made of two identical halves bonded at 30°. The article “Testing the Bond Between Repair Materials and Concrete Substrate” (ACI Materials J., 1996:553–558)
Use the data of Exercise 19 to calculate a 95% CI for the difference between true average stopping distance for cars equipped with system 1 and cars equipped with system 2.Does the interval suggest that precise information about the value of this difference is available?
Let 1 and 2 denote true average densities for two different types of brick. Assuming normality of the two density distributions, test H0: 1 2 0 versus Ha: 1 2 0 using the following data: m 6, x 22.73, s1 .164, n 5, y 21.95, and s2 .240.
To decide whether two different types of steel have the same true average fracture toughness values, n specimens of each type are tested, yielding the following results:
A mechanical engineer wishes to compare strength properties of steel beams with similar beams made with a particular alloy. The same number of beams, n, of each type will be tested. Each beam will be set in a horizontal position with a support on each end, a force of 2500 lb will be applied at the

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