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

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Let a be a number between 0 and 1, and define a sequence by and for . Substituting for its representation in terms of and , then substituting for , and so on, results in The fact that Wt depends not only on but also on averages for past time points, albeit with (exponentially) decreasing weights,
Resistance observations (ohms) for subgroups of a certain type of register gave the following summary quantities:i ni si i ni si 1 4 430.0 22.5 11 4 445.2 27.3 2 4 418.2 20.6 12 4 430.1 22.2 3 3 435.5 25.1 13 4 427.2 24.0 4 4 427.6 22.3 14 4 439.6 23.3 5 4 444.0 21.5 15 3 415.9 31.2 6 3 431.4 28.9
An alternative to the p chart for the fraction defective is the np chart for number defective. This chart has, and the number of defectives from each sample is plotted on the chart.Construct such a chart for the data of Example 16.6. Will the use of an np chart always give the same message as the
The following numbers are observations on tensile strength of synthetic fabric specimens selected from a production process at equally spaced time intervals. Construct appropriate control charts, and comment (assume an assignable cause is identifiable for any out-of-control observations) 1.51.3
The number of scratches on the surface of each of 24 rectangular metal plates is determined, yielding the following data: 8, 1, 7, 5, 2, 0, 2, 3, 4, 3, 1, 2, 5, 7, 3, 4, 6, 5, 2, gr gsi 5 402 i 5 1074 gxi 5 10,980, 4, 0, 10, 2,6.Construct an appropriate control chart, and comment.
Observations on shear strength for 26 subgroups of test spot welds, each consisting of six welds, yield, and . Calculate control limits for any relevant control charts.
Consider the single-sample plan that utilizes and when . Determine the values of AOQ and ATI for selected values of p, and graph each of these against p. Also determine the value of AOQL.
Refer to Example 16.11, in which a single-sample plan with and was employed.a. Calculate AOQ for . What does this suggest about the value of p for which AOQ is a maximum and the corresponding AOQL?b. Determine the value of p for which AOQ is a maximum and the corresponding value of AOQL. [Hint: Use
Some sources advocate a somewhat more restrictive type of doubling-sampling plan in which ; that is, the lot is rejected if at either stage the (total) number of defectives is at least r1 (see the book by Montgomery). Consider this type of sampling plan with , and . Calculate the probability of lot
Consider the double-sampling plan for which both sample sizes are 50.The lot is accepted after the first sample if the number of defectives is at most 1, rejected if the number of LTPD 5 .07 a 5 .05, b 5 .10 AQL 5 .02 c 5 2 p 5 .01, .02,c, .05 n 5 100 p 5 .01, .02,c, 10 p 5 .01, .02,c, .10, N 5 500
Develop a single-sample plan for which and in the case . Once values of n and c have been determined, calculate the achieved values of a and b for the plan.
Refer to Exercise 34 and consider the plan with and . Calculate P(A) for , and sketch the two OC curves on the same set of axes. Which of the two plans is preferable (leaving aside the cost of sampling) and why?
A sample of 50 items is to be selected from a batch consisting of 5000 items. The batch will be accepted if the sample contains at most one defective item. Calculate the probability of lot acceptance for , and sketch the OC curve.
Consider the single-sample plan with and , as discussed in Example 16.11, but now suppose that the lot size is . Calculate P(A), the probability of accepting the lot, for using the hypergeometric distribution. Does the binomial approximation give satisfactory results in this case?
The target value for the diameter of a certain type of driveshaft is .75 in. The size of the shift in the average diameter considered important to detect is .002 in. Sample average diameters for successive groups of shafts are as follows: .7507, .7504, .7492, .7501, .7503, .7510, .7490, n 5 4 5 .10
Construct a control chart for the data of Exercise 25 by using the transformation suggested in the text
In some situations, the sizes of sampled specimens vary, and larger specimens are expected to have more defects than smaller ones. For example, sizes of fabric samples inspected for flaws might vary over time. Alternatively, the number of items inspected might change with time. Let 5 xi gi ui 5 the
For what values will the LCL in a c chart be negative?
Refer to the data of Exercise 22, and construct a control chart using the sin transformation as suggested in the text.
When , what is the smallest value of for which the LCL in a p chart is positive?
When S2 is the sample variance of a normal random sample, has a chi-squared distribution with df, so from which This suggests that an alternative chart for controlling process variation involves plotting the sample variances and using the control limits Construct the corresponding chart for the
Calculate control limits for an S chart from the refractive index data of Exercise 11.Does the process appear to be in control with respect to variability? Why or why not?
The following data on the deviation from target in the parallel orientation is taken from Table 1 of the article cited in Example 16.5. Sometimes a transformation of the data is appropriate, either because of nonnormality or because subgroup variation changes systematically with the subgroup mean.
Calculate control limits for the data of Exercise 8 using the robust procedure presented in this section.
Apply the supplemental rules suggested in the text to the data of Exercise 8.Are there any out-of-control signals?
Consider the control chart based on control limits m . 0 6 2.81 s/ 1na. What is the ARL when the process is in control?b. What is the ARL when and the process mean has shifted to ?c. How do the values of parts (a) and (b) compare to the corresponding values for a 3-sigma chart?m 5 m0 1 s n 5 4
The accompanying table gives sample means and standard deviations, each based on observations of the refractiv index of fiber-optic cable. Construct a control chart, and comment on its appearance. [Hint: and .]Day s Day s 1 95.47 1.30 13 97.02 1.28 2 97.38 .88 14 95.55 1.14 3 96.85 1.43 15 96.29
Refer to Exercises 8 and 9, and now employ control limits based on using the sample ranges to estimate s. Does the process appear to be in control?
The table below gives data on moisture content for specimens of a certain type of fabric. Determine control limits for a chart with center line at height 13.00 based on , construct the control chart, and comment on its appearance.
Consider a 3-sigma control chart with a center line at m0 and based on . Assuming normality, calculate the probability that a single point will fall outside the control limits when the actual process mean is a.b.c.
If a process variable is normally distributed, in the long run virtually all observed values should be between and, giving a process spread of 6s.a. With LSL and USL denoting the lower and upper specification limits, one commonly used process capability index is . Cp 5 (USL 2 LSL)/6s The value Cp 5
A cork intended for use in a wine bottle is considered acceptable if its diameter is between 2.9 cm and 3.1 cm (so the lower specification limit is and the upper specification limit is ).a. If cork diameter is a normally distributed variable with mean value 3.04 cm and standard deviation .02 cm,
The ranking procedure described in Exercise 35 is somewhat asymmetric, because the smallest observation receives rank 1, whereas the largest receives rank 2, and so on. Suppose both the smallest and the largest receive rank 1, the second smallest and second largest receive rank 2, and so on, and
Refer to Exercise 33, and consider a confidence interval associated with the sign test: the sign interval. The relevant hypotheses are now versus .Let’s use the following rejection region: either or.a. What is the significance level for this test?b. The confidence interval will consist of all
The sign test is a very simple procedure for testing hypotheses about a population median assuming only that the underlying distribution is continuous. To illustrate, consider the following sample of 20 observations on component lifetime (hr):1.7 3.3 5.1 6.9 12.6 14.4 16.4 24.6 26.0 26.5 32.1 37.4
The given data on phosphorus concentration in topsoil for four different soil treatments appeared in the article “Fertilisers for Lotus and Clover Establishment on a Sequence of Acid Soils on the East Otago Uplands” (N. Zeal. J. of Exptl. Ag., 1984:119–129). Use a distribution-free procedure
High-pressure sales tactics or door-to-door salespeople can be quite offensive. Many people succumb to such tactics, sign a purchase agreement, and later regret their actions. In the mid-1970s, the Federal Trade Commission implemented regulations clarifying and extending the rights of purchasers to
In an experiment to study the way in which different anesthetics affect plasma epinephrine concentration, ten dogs were selected and concentration was measured while they were under the influence of the anesthetics isoflurane, halothane, and cyclopropane (“Sympathoadrenal and Hemodynamic Effects
In a test to determine whether soil pretreated with small amounts of Basic-H makes the soil more permeable to water, soil samples were divided into blocks, and each block received each of the four treatments under study. The treatments were (A) water with .001% Basic-H flooded on control soil, (B)
The accompanying data on cortisol level was reported in the article “Cortisol, Cortisone, and 11-Deoxycortisol Levels in Human Umbilical and Maternal Plasma in Relation to the Onset of Labor” (J. of Obstetric Gynaecology of the British Commonwealth, 1974: 737–745). Experimental subjects were
The article “Production of Gaseous Nitrogen in Human Steady-State Conditions” (J. of Applied Physiology, 1972:155–159) reports the following observations on the amount of nitrogen expired (in liters) under four dietary regimens:(1) fasting, (2) 23% protein, (3) 32% protein, and (4)
The accompanying data refers to concentration of the radioactive isotope strontium-90 in milk samples obtained from five randomly selected dairies in each of four different regions.1 6.4 5.8 6.5 7.7 6.1 Region 2 7.1 9.9 11.2 10.5 8.8 3 5.7 5.9 8.2 6.6 5.1 4 9.5 12.1 10.3 12.4 11.7 Test at level .10
Compute a 99% CI for using the data in Exercise 11.
Compute the 90% rank-sum CI for using the data in Exercise 10.
An experiment was carried out to compare the abilities of two different solvents to extract creosote impregnated in test logs. Each of eight logs was divided into two segments, and then one segment was randomly selected for application of the first solvent, with the other segment receiving the
Reconsider the situation described in Exercise 81 of Chapter 9 and the accompanying Minitab output (the Greek letter eta is used to denote a median).Mann-Whitney Confidence Interval and Test good poor Point estimate for ETA1-ETA2 is 95.9 Percent CI for ETA1-ETA2 is ( )Test of vs is significant at
The accompanying data resulted from an experiment to compare the effects of vitamin C in orange juice and in synthetic ascorbic acid on the length of odontoblasts in guinea pigs over a 6-week period (“The Growth of the Odontoblasts of the Incisor Tooth as a Criterion of the Vitamin C Intake of
A modification has been made to the process for producing a certain type of “time-zero” film (film that begins to develop as soon as a picture is taken). Because the modification involves extra cost, it will be incorporated only if sample data strongly indicates that the modification has
The article “A Study of Wood Stove Particulate Emissions”(J. of the Air Pollution Control Assoc., 1979: 724–728)reports the following data on burn time (hours) for samples of oak and pine. Test at level .05 to see whether there is any difference in true average burn time for the two types of
In an experiment to compare the bond strength of two different adhesives, each adhesive was used in five bondings of two surfaces, and the force necessary to separate the surfaces was determined for each bonding. For adhesive 1, the resulting values were 229, 286, 245, 299, and 250, whereas the
Suppose that observations are made on a process at times . On the basis of this data, we wish to test 1, 2,c, n X1, X2, c,H0: the Xi ’s constitute an independent and identically distributed sequence versus Ha: tends to be larger than Xi for (an increasing trend)Suppose the Xi ’s are ranked from
Reconsider the port alcohol content data from Exercise 14.22. A normal probability plot casts some doubt on the assumption of population normality. However, a dotplot shows a reasonable amount of symmetry, and the mean, median, and 5% trimmed mean are 19.257, 19.200, and 19.209, respectively. Use
Reconsider the situation described in Exercise 39 of Section 9.3, and use the Wilcoxon test to test the appropriate hypotheses.
Here again is the data on expense ratio (%) for a sample of 20 large-cap blended mutual funds introduced in Exercise 1.53:1.03 1.23 1.10 1.64 1.30 1.27 1.25.78 1.05 .64 .94 .86 1.05 .75.09 0.79 1.61 1.26 .93 .84 A normal probability plot shows a distinctly nonlinear pattern, primarily because of
Reconsider the situation described in Exercise 34 of Section 8.2, and use the Wilcoxon test with to test the relevant hypotheses.
The Fibonacci sequence of numbers occurs in various scientific contexts. The first two numbers in the sequence are 1,1. Then every succeeding number is the sum of the two previous numbers: 1, 1, 1 1 2, 1 2 3, 2 3 5, 8, 13, 21, . . .. The first digit of any number in this sequence can be
Do the successive digits in the decimal expansion of p behave as though they were selected from a random number table (or came from a computer’s random number generator)?a. Let p0 denote the long run proportion of digits in the expansion that equal 0, and define analogously. What hypotheses about
Have you ever wondered whether soccer players suffer adverse effects from hitting “headers”? The authors of the article “No Evidence of Impaired Neurocognitive Performance in Collegiate Soccer Players” (Amer. J. of Sports Med., 2002: 157–162) investigated this issue from several
The NCAA basketball tournament begins with 64 teams that are apportioned into four regional tournaments, each involving 16 teams. The 16 teams in each region are then ranked (seeded) from 1 to 16.During the 12-year period from 1991 to 2002, the top-ranked team won its regional tournament 22 times,
Let p1 denote the proportion of successes in a particular population. The test statistic value in Chapter 8 for testing was , where. Show that for the case , the chisquared test statistic value of Section 14.1 satisfies .[Hint: First show that .]
In a study to investigate the extent to which individuals are aware of industrial odors in a certain region(“Annoyance and Health Reactions to Odor from Refineries and Other Industries in Carson, California,”Environmental Research, 1978: 119–132), a sample of a 5 .05(P , .015)individuals was
Much attention has recently focused on the incidence of concussions among athletes. Separate samples of soccer players, non-soccer athletes, and non-athletes were selected. The accompanying table then resulted from determining the number of concussions each individual reported on a medical history
The accompanying two-way frequency table appears in the article “Marijuana Use in College” (Youth and Society, 1979: 323–334). Each of 445 college students was classified according to both frequency of marijuana use and parental use of alcohol and psychoactive drugs.Does the data suggest that
The authors of the article “Predicting Professional Sports Game Outcomes from Intermediate Game Scores” (Chance, 1992: 18–22) used a chi-squared test to determine whether there was any merit to the idea that basketball games are not settled until the last quarter, whereas baseball games are
Qualifications of male and female head and assistant college athletic coaches were compared in the article “Sex Bias and the Validity of Believed Differences Between Male and Female Interscholastic Athletic Coaches” (Research Quarterly for Exercise and Sport, 1990: 259–267). Each person in
Does the phase of the moon have any bearing on birthrate?Each of 222,784 births that occurred during a period encompassing 24 full lunar cycles was classified according to lunar phase. The following data is consistent with summary quantities that appeared in the article “The Effect of the Lunar
Consider the accompanying table displaying the sample proportions that fell in the various combinations of categories (e.g., 13% of those in the sample were in the first category of both factors).123 1 .13 .19 .28 2 .07 .11 .22 2 3 3 nijk eˆ ’s ijk pˆijka. Suppose the sample consisted of
Suppose that in a particular state consisting of four distinct regions, a random sample of nk voters is obtained from the k th region for . Each voter is then classified according to which candidate (1, 2, or 3) he or she prefers and according to voter registration. Let denote the proportion of
Suppose that in Exercise 32 each student had been categorized with respect to political views, marijuana usage, and religious preference, with the categories of this latter factor being Protestant, Catholic, and other. The data could be displayed in three different two-way tables, one corresponding
Each individual in a random sample of high school and college students was cross-classified with respect to both political views and marijuana usage, resulting in the data displayed in the accompanying two-way table (“Attitudes About Marijuana and Political Views,” Psychological Reports, 1973:
A random sample of smokers was obtained, and each individual was classified both with respect to gender and with respect to the age at which he/she first started smoking. The data in the accompanying table is consistent with summary results reported in the article “Cigarette Tar Yields in
Three different design configurations are being considered for a particular component. There are four possible failure modes for the component. An engineer obtained the following data on number of failures in each mode for each of the three configurations. Does the configuration appear to have an
The accompanying data on degree of spirituality for samples of natural and social scientists at research universities as well as for a sample of non-academics with graduate degrees appeared in the article “Conflict Between Religion and Science Among Academic Scientists” (J. for the Scientific
A random sample of 175 Cal Poly State University students was selected, and both the email service provider and cell phone provider were determined for each one, resulting in the accompanying data. State and test the appropriate hypotheses using the P-value approach.
The article “Human Lateralization from Head to Foot: SexRelated Factors” (Science, 1978: 1291–1292) reports for both a sample of right-handed men and a sample of right-handed women the number of individuals whose feet were the same size, had a bigger left than right foot (a difference of half
The accompanying data refers to leaf marks found on white clover samples selected from both long-grass areas and short-grass areas (“The Biology of the Leaf Mark Polymorphism in Trifolium repens L.,” Heredity, 1976: 306–325).Use a x2 test to decide whether the true proportions of different
The accompanying two-way table was constructed using data in the article “Television Viewing and Physical Fitness in Adults” (Research Quarterly for Exercise and Sport, 1990: 315–320). The author hoped to determine whether time spent watching television is associated with cardiovascular
The article from which the data in Exercise 20 was obtained also gave the accompanying data on the composite mass/outer fabric mass ratio for high-quality fabric specimens.
The article “Nonbloated Burned Clay Aggregate Concrete”(J. of Materials, 1972: 555–563) reports the following data on 7-day flexural strength of nonbloated burned clay aggregate concrete samples (psi):257 327 317 300 340 340 343 374 377 386 383 393 407 407 434 427 440 407 450 440 456 460 456
The article “A Method for the Estimation of Alcohol in Fortified Wines Using Hydrometer Baumé and Refractometer Brix” (Amer. J. of Enol. and Vitic., 2006:486–490) gave duplicate measurements on distilled alcohol content (%) for a sample of 35 port wines. Here are averages of those duplicate
An article in Annals of Mathematical Statistics reports the following data on the number of borers in each of 120 groups of borers. Does the Poisson pmf provide a rigidity for medium-quality fabric specimens, from which the accompanying Minitab output was obtained:24.6 12.7 14.4 30.6 16.1 9.5 31.5
In a genetics experiment, investigators looked at 300 chromosomes of a particular type and counted the number of sister-chromatid exchanges on each (“On the Nature of Sister-Chromatid Exchanges in 5-BromodeoxyuridineSubstituted Chromosomes,” Genetics, 1979: 1251–1264). A Poisson model was
The article “Compatibility of Outer and Fusible Interlining Fabrics in Tailored Garments (Textile Res. J., 1997:137–142) gave the following observations on bendingˆu1, ˆu2'/'u ' 2 /'u1 pi(u1, u2)H0: p1 5 p1(u1, u2),c, p6 5 p6(u1, u2)p6 5 2u2(1 2 u1 2 u2)p4 5 2u1u2 p5 5 2u1(1 2 u1 2 u2)p1 5 u1
Each headlight on an automobile undergoing an annual vehicle inspection can be focused either too high (H), too low (L), or properly (N). Checking the two headlights simultaneously (and not distinguishing between left and right) results in the six possible outcomes HH, LL, NN, HL, HN, and LN. If
The article “A Probabilistic Analysis of Dissolved Oxygen–Biochemical Oxygen Demand Relationship in Streams” (J. Water Resources Control Fed., 1969: 73–90)reports data on the rate of oxygenation in streams at 20°C in a certain region. The sample mean and standard deviation were computed as
A certain type of flashlight is sold with the four batteries included. A random sample of 150 flashlights is obtained, and the number of defective batteries in each is determined, resulting in the following data:Number Defective 01234 Frequency 26 51 47 16 10 Let X be the number of defective
The article “Feeding Ecology of the Red-Eyed Vireo and Associated Foliage-Gleaning Birds” (Ecological Monographs, 1971: 129–152) presents the accompanying data on the variable the number of hops before the first flight and preceded by a flight. The author then proposed and fit a geometric
A study of sterility in the fruit fly (“Hybrid Dysgenesis in Drosophila melanogaster: The Biology of Female and Male Sterility,” Genetics, 1979: 161–174) reports the following data on the number of ovaries developed by each female fly in a sample of size 1388. One model for unilateral
Consider a large population of families in which each family has exactly three children. If the genders of the three children in any family are independent of one another, the number of male children in a randomly selected family will have a binomial distribution based on three trials.a. Suppose a
a. Show that another expression for the chi-squared statistic is Why is it more efficient to compute x2 using this formula?b. When the null hypothesis is(i.e., for all i), how does the formula of part (a) simplify? Use the simplified expression to calculate x2 for the pigeon/direction data in
The response time of a computer system to a request for a certain type of information is hypothesized to have an exponential distribution with parameter sec (so if, the pdf of X under H0 is for).a. If you had observed and wanted to use the chi-squared test with five class intervals having equal
The article “The Gap Between Wine Expert Ratings and Consumer Preferences” (Intl. J. of Wine Business Res., 2008: 335–351) studied differences between expert and consumer ratings by considering medal ratings for wines, which could be gold (G), silver (S), or bronze (B). Three categories were
It is hypothesized that when homing pigeons are disoriented in a certain manner, they will exhibit no preference for any direction of flight after takeoff (so that the direction X should be uniformly distributed on the interval from 0° to 360°). To test this, 120 pigeons are disoriented, let
The article “Racial Stereotypes in Children’s Television Commercials” (J. of Adver. Res., 2008: 80–93) reported the following frequencies with which ethnic characters appeared in recorded commercials that aired on Philadelphia television stations.African Ethnicity: American Asian Caucasian
Say as much as you can about the P-value for an upper-tailed chi-squared test in each of the following situations:a. b.c. d.e.
What conclusion would be appropriate for an upper-tailed chi-squared test in each of the following situations?a.b.c.d.
Given that for the model containing predictors x1, x4, x5, and x8 and for the model with predictors x1, x3, x5, and x6, what can you say about R2 for the model containing predictorsa. x1, x3, x4, x5, x6, and x8? Explain.b. x1 and x4? Explain.
Does exposure to air pollution result in decreased life expectancy? This question was examined in the article“Does Air Pollution Shorten Lives?” (Statistics and Public Policy, Reading, MA, Addison-Wesley, 1977). Data on for the year 1960 was recorded for randomly selected standard metropolitan
A sample of companies was selected, and the values of price and variables (such as quarterly dividend, previous year’s earnings, and debt ratio) were determined. When the multiple regression model using these 15 predictors was fit to the data, resulted.a. Does the model appear to specify a useful
Coir fiber, derived from coconut, is an eco-friendly material with great potential for use in construction. The article“Seepage Velocity and Piping Resistance of Coir Fiber Mixed Soils” (J. of Irrig. and Drainage Engr., 2008:485–492) included several multiple regression analyses.The

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

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