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introduction to probability statistics

Probability And Statistics For Engineering And The Sciences 8th Edition Jay L Devore, Roger Ellsbury - Solutions

Reconsider Example 10.8 involving an investigation of the effects of different heat treatments on the yield point of steel ingots.a. If and , what is b for a level .05 F test when, and ?b. For the alternative of part (a), what value of J is necessary to obtain ?c. If there are heat treatments, ,
When sample sizes are equal , the parameters of the alternative parameterization are restricted by . For unequal sample sizes, the most natural restriction is . Use this to show that What is E(MSTr) when H0 is true? [This expectation is correct if is replaced by the restriction (or any other single
For a single-factor ANOVA with sample sizes, show that where .
Lipids provide much of the dietary energy in the bodies of infants and young children. There is a growing interest in the quality of the dietary lipid supply during infancy as a major determinant of growth, visual and neural development, and long-term health. The article “Essential Fat
The accompanying summary data on skeletal-muscle CS activity (nmol/min/mg) appeared in the article “Impact of Lifelong Sedentary Behavior on Mitochondrial Function of Mice Skeletal Muscle” (J. of Gerontology, 2009: 927–939):Old Old Young Sedentary Active Sample size 10 8 10 Sample mean 46.68
Apply the modified Tukey’s method to the data in Exercise 22 to identify significant differences among the mi’s.a 5 .05 5 1.6, 3.8, 6.0
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 , 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 49.0 10.2: 44.6
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 injection
Refer to Exercise 19 and suppose , and. Can you now find a value of SSE that produces such a contradiction between the F test and Tukey’s procedure?
Consider a single-factor ANOVA experiment in which, , and . Find a value of SSE for which , so that is rejected, yet when Tukey’s procedure is applied none of the mi’s can be said to differ significantly from one another.
Consider the accompanying data on plant growth after the application of five different types of growth hormone.1: 13 17 7 14 2: 21 13 20 17 3: 18 15 20 17 4: 7 11 18 10 5: 6 11 15 8a. Perform an F test at level .b. What happens when Tukey’s procedure is applied?
Refer to Exercise 5.Compute a 95% t CI for.
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
Exercise 10.7 described an experiment in which 26 resistivity observations were made on each of six different concrete mixtures. The article cited there gave the following sample means: 14.18, 17.94, 18.00, 18.00, 25.74, 27.67. Apply Tukey’s method with a simultaneous confidence level of 95% to
Repeat Exercise 12 supposing that in addition to .
In Exercise 11, suppose . 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.
An experiment to compare the spreading rates of five different brands of yellow interior latex paint available in a particular area used 4 gallons of each paint. The sample average spreading rates for the five brands were , and . The computed value of F was found to be significant at level . With ,
In single-factor ANOVA with I treatments and J observations per treatment, let .a. Express in terms of m. [Hint: ]b. Determine . [Hint: For any rv Y,.]c. Determine .d. Determine E(SSTr) and then show thate. Using the result of part (d), what is E(MSTr) when H0 is true? When H0 is false, how does
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 (mg/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
A study of the properties of metal plate-connected trusses used for roof support (“Modeling Joints Made with LightGauge 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:4:
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: 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 23.7 34.0 17.1 26.8 23.7 24.9 3: 29.5 34.0 27.5 29.4 27.9
Consider the following summary data on the modulus of elasticity ( 106 psi) for lumber of three different grades [in close agreement with values in the article “Bending Strength and Stiffness of Second-Growth Douglas-Fir Dimension Lumber” (Forest Products J., 1991: 35–43), except that the
It is common practice in many countries to destroy (shred)refrigerators at the end of their useful lives. In this process material from insulating foam may be released into the atmosphere. The article “Release of Fluorocarbons from Insulation Foam in Home Appliances during Shredding”(J. of the
The lumen output was determined for each of different brands of 60-watt soft-white lightbulbs, with bulbs of each brand tested. The sums of squares were computed as and . State the hypotheses of interest (including word definitions of parameters), and use the F test of ANOVA to decide whether there
Suppose that the compression-strength observations on the fourth type of box in Example 10.1 had been 655.1, 748.7, 662.4, 679.0, 706.9, and 640.0 (obtained by adding 120 to each previous ). Assuming no change in the remaining observations, carry out an F test with .
In an experiment to compare the tensile strengths of different types of copper wire, samples of each type were used. The between-samples and within-samples estimates of s2 were computed as and, respectively.a. Use the F test at level .05 to test versus Ha: at least two mi’s are unequal.b. What
Referring to Exercise 94, develop a large-sample confidence interval formula for . Calculate the interval for the data given there using a confidence level of 95%.
Let be a random sample from a Poisson distribution with parameter m1, and let be a random sample from another Poisson distribution with parameter m2. We wish to test against one of the three standard alternatives. When m and n are large, the large-sample z test of Section 9.1 can be used. However,
The article “Evaluating Variability in Filling Operations”(Food Tech., 1984: 51–55) describes two different filling operations used in a ground-beef packing plant. Both filling operations were set to fill packages with 1400 g of ground beef. In a random sample of size 30 taken from each
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 2.Then X1 is the number of pairs in which both treatments were successful, and similarly for X2,
Researchers sent 5000 resumes in response to job ads that appeared in the Boston Globe and Chicago Tribune. The resumes were identical except that 2500 of them had “white sounding” first names, such as Brett and Emily, whereas the other 2500 had “black sounding” names such as Tamika and
The following data refers to airborne bacteria count (number of colonies/ft3) both for carpeted hospital rooms and for uncarpeted rooms (“Microbial Air Sampling in a Carpeted Hospital,” J. of Environmental Health, 1968: 405). Does there appear to be a difference in true average bacteria count
Suppose a level .05 test of versus is to be performed, assuming and normality of both distributions, using equal sample sizes . Evaluate the probability of a type II error when and , and 10,000.Can you think of real problems in which the difference has little practical significance? Would sample
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 between the
Wait staff at restaurants have employed various strategies to increase tips. An article in the Sept. 5, 2005, 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 tip
An experimenter wishes to obtain a CI for the difference between true average breaking strength for cables manufactured by company I and by company II. Suppose breaking strength is normally distributed for both types of cable with psi and psi.a. If costs dictate that the sample size for the type I
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
Arsenic is a known carcinogen and poison. The standard laboratory procedures for measuring arsenic concentration(mg/L) in water are expensive. Consider the accompanying summary data and Minitab output for comparing a laboratory method to a new relatively quick and inexpensive field method (from the
The article “The Accuracy of Stated Energy Contents of Reduced-Energy, Commercially Prepared Foods” (J. of the Amer. Dietetic Assoc., 2010: 116–123) presented the accompanying data on vendor-stated gross energy and measured value (both in kcal) for 10 different supermarket convenience
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
Information about hand posture and forces generated by the fingers during manipulation of various daily objects is needed for designing high-tech hand prosthetic devices. The article “Grip Posture and Forces During Holding Cylindrical Objects with Circular Grips” (Ergonomics, 1996: 1163–
The article “Fatigue Testing of Condoms” cited in Exercise 7.32 reported that for a sample of 20 natural latex condoms of a certain type, the sample mean and sample standard deviation of the number of cycles to break were 4358 and 2218, respectively, whereas a sample of 20 polyisoprene condoms
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 article “Urban Battery Litter” cited in Example 8.14 gave the following summary data on zinc mass (g) for two different brands of size D batteries:Assuming that both zinc mass distributions are at least approximately normal, carry out a test at significance level .05 using the P-value
The article “Quantitative MRI and Electrophysiology of Preoperative Carpal Tunnel Syndrome in a Female Population” (Ergonomics, 1997: 642–649) reported that( .3, 1691.9) was a large-sample 95% confidence interval for the difference between true average thenar muscle volume (mm3) for sufferers
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. of the Geotechnical Division, Am. Soc. Civil Engrs.Proceedings, 1981: 563–576). Before cyclic strength testing,
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 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 between the
The article “Enhancement of Compressive Properties of Failed Concrete Cylinders with Polymer Impregnation”(J. of Testing and Evaluation, 1977: 333–337) reports the following data on impregnated compressive modulus( ) when two different polymers were used to repair cracks in failed
In a study of copper deficiency in cattle, the copper values(mg 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
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.v f 5 3.24 1 5 35, v2 5 20
Give as much information as you can about the P-value of the F test in each of the following situations:a. , upper-tailed test,b. , upper-tailed test,c. v , two-tailed test, f 5 5.64 1 5 5, v2 5 10 v1 5 5, v2 5 10 f 5 2.00 v1 5 5, v2 5 10 f 5 4.75 v1 5 10, v P(.177 # F # 4.74) 2 5 5 v1 5 6, v P(F #
Obtain or compute the following quantities:a.b. c. d.e. The 99th percentile of the F distribution withf. The 1st percentile of the F distribution with g. for h. for
Using the traditional formula, a 95% CI for is to be constructed based on equal sample sizes from the two populations. For what value of will the resulting interval have a width at most of .1, irrespective of the results of the sampling?
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
Sometimes experiments involving success or failure responses are run in a paired or before/after manner.Suppose that before a major policy speech by a political candidate, n individuals are selected and asked whether (S)or not (F) they favor the candidate. Then after the speech the same n people
In medical investigations, the ratio is often of more interest than the difference (e.g., individuals given treatment 1 are how many times as likely to recover as those given treatment 2?). Let . When m and n are both large, the statistic has approximately a normal distribution with approximate
Teen Court is a juvenile diversion program designed to circumvent the formal processing of first-time juvenile offenders within the juvenile justice system. The article “An Experimental Evaluation of Teen Courts” (J. of Experimental Criminology, 2008: 137–163) reported on a study in which
Olestra is a fat substitute approved by the FDA for use in snack foods. Because there have been anecdotal reports of gastrointestinal problems associated with olestra consumption, a randomized, double-blind, placebo-controlled experiment was carried out to compare olestra potato chips to regular
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 Sciences, 1991: 67–76) tested this theory by
Recent incidents of food contamination have caused great concern among consumers. The article “How Safe Is That Chicken?” (Consumer Reports, Jan. 2010: 19–23) reported that 35 of 80 randomly selected Perdue brand broilers tested positively for either campylobacter or salmonella (or both), the
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.
Construct a paired data set for which , so that the data is highly significant when the correct analysis is used, yet t for the two-sample t test is quite near zero, so the incorrect analysis yields an insignificant result.
The paper “Slender High-Strength RC Columns Under Eccentric Compression” (Magazine of Concrete Res., 2005:361–370) gave the accompanying data on cylinder strength(MPa) for various types of columns cured under both moist conditions and laboratory drying conditiona. Estimate the difference in
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 specp 5 .033(p 5 0.003, t value 5 3.65)5 2227.8(96.6)Mean (6 SD) 5
Refer back to the previous exercise.a. By far the most frequently tested null hypothesis when data is paired is . Is that a sensible hypothesis in this context? Explain.b. Carry out a test of hypotheses to decide whether there is compelling evidence for concluding that on average diagnosis occurs
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 (months) for 15 children suffering from the
It has been estimated that between 1945 and 1971, as many as 2 million children were born to mothers treated with diethylstilbestrol (DES), a nonsteroidal estrogen recommended for pregnancy maintenance. The FDA banned this drug in 1971 because research indicated a link with the incidence of
Antipsychotic drugs are widely prescribed for conditions such as schizophrenia and bipolar disease. The article “Cardiometabolic Risk of Second-Generation Antipsychotic Medications During First-Time Use in Children and Adolescents” (J. of the Amer. Med. Assoc., 2009) reported on body
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. of Clinical Nutr., 2004: 1322–1326) gave the following data on
Scientists and engineers frequently wish to compare two different techniques for measuring or determining the value of a variable. In such situations, interest centers on testing whether the mean difference in measurements is zero. The article “Evaluation of the Deuterium Dilution Technique
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 when both population distributions are normal with . Then use this test procedure to test the hypotheses suggested in Exercise 33.
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.a. Assuming that the underlying distributions are normal, calculate and interpret a 99% CI
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 Investigate and Monitor Bird Behavior and Damage to Vineyards” (Amer. J. of Enology and Viticulture, 2004:288–291) reported on an experiment involving a bird-feeder table,
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
Quantitative noninvasive techniques are needed for routinely assessing symptoms of peripheral neuropathies, such as carpal tunnel syndrome (CTS). The article “A Gap Detection Tactility Test for Sensory Deficits Associated with Carpal Tunnel Syndrome” (Ergonomics, 1995:2588–2601) reported on a
Suppose m1 and m2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. Use the two-sample t test at significance level .01 to test versus for the following data:, and .
Let m1 and m2 denote true average densities for two different types of brick. Assuming normality of the two density distributions, test versus using the following data:, and .
Determine the number of degrees of freedom for the twosample t test or CI in each of the following situations:a.b.c.d.
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 Calculate the P-value for the appropriate two-sample z test, assuming that the data was based on . Then repeat the calculation for
a. Show for the upper-tailed test with s1 and s2 known that as either m or n increases, b decreases whenb. For the case of equal sample sizes and fixed a, what happens to the necessary sample size n as b is decreased, where b is the desired type II error probability at a fixed alternative?
The level of monoamine oxidase (MAO) activity in blood platelets (nm/mg protein/h) was determined for each individual in a sample of 43 chronic schizophrenics, resulting in and , as well as for 45 normal subjects, resulting in and . Does this data strongly suggest that true average MAO activity for
The accompanying table gives summary data on cube compressive strength (N/mm2) for concrete specimens made with a pulverized fuel-ash mix (“A Study of Twenty-FiveYear-Old Pulverized Fuel Ash Concrete Used in Foundation Structures,” Proc. Inst. Civ. Engrs., Mar. 1985: 149–165)Calculate and
The level of lead in the blood was determined for a sample of 152 male hazardous-waste workers ages 20–30 and also for a sample of 86 female workers, resulting in a mean standard error of for the men and for the women (“Temporal Changes in Blood Lead Levels of Hazardous Waste Workers in New
An experiment was performed to compare the fracture toughness of high-purity 18 Ni maraging steel with commercial-purity steel of the same type (Corrosion Science, 1971: 723–736). For specimens, the sample average toughness was for the high-purity steel, whereas for specimens of commercial steel.
Tensile-strength tests were carried out on two different grades of wire rod (“Fluidized Bed Patenting of Wire Rods,” Wire J., June 1977: 56–61), resulting in the accompanying data.Sample Sample Mean Sample Grade Size (kg/mm2) SD AISI 1064 AISI 1078a. Does the data provide compelling evidence
Is there any systematic tendency for part-time college faculty to hold their students to different standards than do full-time faculty? The article “Are There Instructional Differences Between Full-Time and Part-Time Faculty?” (College Teaching, 2009: 23–26) reported that for a sample of 125
An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in for the modified mortar and for the unmodified mortar . Let m1 and m2 be the true
Persons having Reynaud’s syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For subjects with the
a. Use the data of Example 9.4 to compute a 95% CI for. Does the resulting interval suggest that has been precisely estimated?b. Use the data of Exercise 3 to compute a 95% upper confidence bound for .
Let m1 denote true average tread life for a premium brand of P205/65R15 radial tire, and let m2 denote the true average tread life for an economy brand of the same size. Test versus at level.01, using the following data:, and .
The National Health Statistics Reports dated Oct. 22, 2008, included the following information on the heights (in.) for non-Hispanic white females:a. Calculate and interpret a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger
An article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively.Suppose these are the population average lifetimes.a. Let be
After a period of apprenticeship, an organization gives an exam that must be passed to be eligible for membership. Let(randomly chosen apprentice passes). The organization wishes an exam that most but not all should be able to pass, so it decides that is desirable. For a particular exam, the
Suppose the population distribution is normal with known s. Let g be such that . For testing versus , consider the test that rejects H0 if either or , where the test statistic is.a. Show that .b. Derive an expression for . [Hint: Express the test in the form “reject H0 if either .”]c. Let . For
Let be a random sample from an exponential distribution with parameter l. Then it can be shown that has a chi-squared distribution with (by first showing that has a chi-squared distribution with ).a. Use this fact to obtain a test statistic and rejection region that together specify a level a test

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