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Statistics For Engineers And Scientists 4th Edition William Navidi - Solutions
Refer to Example 2.54.a. Find Cov(X,Y).b. Find ρX,Y.
For continuous random variables X and Y with joint probability density function.a. Find P(X > 1 and Y > 1).b. Find the marginal probability density functions fX (x) and fY (y).c. Are X and Y independent? Explain хе-«+ху) х > 0 and y > 0 f (x) = otherwise
A computer sends a packet of information along a channel and waits for a return signal acknowledging that the packet has been received. If no acknowledgment is received within a certain time, the packet is re-sent. Let X represent the number of times the packet is sent. Assume that the probability
A sample of 100 components is drawn, and a 95% confidence interval for the proportion defective specifies this proportion to within ± 0.06. To get a more precise estimate of the number defective, the sample size will be increased to 400, and the confidence interval will be recomputed. What will be
Ten samples of coal from a Northern Appalachian source had an average mercury content of 0.242 ppm with a standard deviation of 0.031 ppm. Find a 95% confidence for the mean mercury content of coal from this source.
Polychlorinated biphenyls (PCBs) are a group of synthetic oil-like chemicals that were at one time widely used as insulation in electrical equipment and were discharged into rivers. They were discovered to be a health hazard and were banned in the 1970s. Since then, much effort has gone into
A pollster plans to survey a random sample of voters in a certain city to ask whether they support an increase in property taxes to fund the construction of a new elementary school. How many voters should be sampled to be sure that a 95% confidence interval for the proportion who favor the proposal
A general method for finding a confidence interval for the difference between two means of normal populations is given by expression (5.21) on page 365. A pooled method that can be used when the variances of the populations are known to be equal is given by expression (5.22) on page 367. This
The article “Toward a Lifespan Metric of Reading Fluency” (S. Wallot and G. Van Orden, International Journal of Bifurcation and Chaos, 2011:1173–1192) described a study of reading speed for undergraduate and graduate students. In a sample of 24 undergraduates, the mean time to read a certain
A chemist made eight independent measurements of the melting point of tungsten. She obtained a sample mean of 3410.14 degrees Celsius and a sample standard deviation of 1.018 degrees.a. Use the Student’s t distribution to find a 95% confidence interval for the melting point of tungsten.b. Use the
Six measurements were made of the mineral content (in percent) of spinach, with the following results.Assuming the population to be normally distributed, construct a 99% confidence interval for population variance σ2. 19.1 20.8 20.8 21.4 20.5 19.7
A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed. Find a 99%
This exercise continues the study of the robustness of the Student€™s t method for constructing confidence intervals. The following figure shows graphs of probability density functions for the N(0, 1) distribution, the lognormal distribution with μ = 1 and σ2=
Refer to Exercise 7. Someone suggests that the paired design be replaced with a design in which 18 cars are sampled, the lifetime of the front brakes is measured on 9 of them, and the lifetime of the rear brakes is measured on the other 9. A confidence interval for the difference between the means
The article “Dynamics of Insulin Action in Hypertension: Assessment from Minimal Model Interpretation of Intravenous Glucose Tolerance Test Data” (R. Burattini, M. Morettini, et al., Med Biol Eng Comput, 2011:831–841) compared levels of an insulin sensitivity index SI in patients with high
Refer to Exercise 5. Additional pieces of yarn will be sampled in order to improve the precision of the confidence interval. Which would increase the precision the most: sampling 50 additional pieces of yarn from the old batch, 50 additional pieces from the new batch, or 25 additional pieces from
The article €œWind-Uplift Capacity of Residential Wood Roof-Sheathing Panels Retrofitted with Insulating Foam Adhesive€ (P. Datin, D. Prevatt, and W. Pang, Journal of Architectural Engineering, 2011:144€“154) presents a study of the failure pressures of roof panels.
A sample of 87 glass sheets has a mean thickness of 4.20 mm with a standard deviation of 0.10 mm.a. Find a 98% confidence interval for the population mean thickness.b. What is the level of the confidence interval (4.185, 4.215)?c. How many glass sheets must be sampled so that a 98% confidence
Six measurements were made of the concentration (in percent) of ash in a certain variety of spinach. The sample mean was 19.35 and the sample standard deviation was 0.577. Assume that the concentrations are normally distributed.a. Find a 90% prediction interval for a single measurement.b. Find a
Find the following values.a. χ212,.025b. χ212,.975c. χ25,.005d. χ25,.995e. χ222,.1f. χ222,.9
In the lettuce yield example presented on page 499, would it be a good idea to use the t test described in Section 6.7 to determine whether the fertilizers differ in their effects on yield? Why or why not?
If the sample size remains the same, and the level α increases, then the power will. Options: increase, decrease.
The article “Evaluation of Criteria for Setting Speed Limits on Gravel Roads” (S. Dissanayake, Journal of Transportation Engineering, 2011:57–63) measured speeds of vehicles on several roads in the state of Kansas. On South Cedar Niles, 73 vehicles were observed, and 49 of
The Mastic tree (Pistacia lentiscus) is used in reforestation efforts in southeastern Spain. The article €œNutrient Deprivation Improves Field Performance of Woody Seedlings in a Degraded Semi-arid Shrubland€ (R. Trubata, J. Cortina, and A. Vilagrosaa, Ecological Engineering,
The article “Influence of Penetration Rate on Penetrometer Resistance” (G. Gagnon and J. Doubrough, Canadian Journal of Civil Engineering, 2011:741–750) describes a study in which twenty 2-L specimens of water were drawn from a public works building in Bridgewater, Nova Scotia. The mean lead
The article “Application of Surgical Navigation to Total Hip Arthroplasty” (T. Ecker and S. Murphy, Journal of Engineering in Medicine, 2007:699–712) reports that in a sample of 113 people undergoing a certain type of hip replacement surgery on one hip, 65 of them had surgery on their right
The article €œThe Effectiveness of Child Restraint Systems for Children Aged 3 Years or Younger During Motor Vehicle Collisions: 1996 to 2005€ (T. Rice and C. Anderson, American Journal of Public Health, 2009:252€“257) studied a large number of automobile accidents
George performed a hypothesis test. Luis checked George’s work by redoing the calculations. Both George and Luis agree that the result was statistically significant at the 5% level, but they got different P-values. George got a P-value of 0.20 and Luis got a P-value of 0.02.a. Is possible that
Two machines used to fill soft drink containers are being compared. The number of containers filled each minute is counted for 60 minutes for each machine. During the 60 minutes, machine 1 filled an average of 73.8 cans per minute with a standard deviation of 5.2 cans per minute, and machine 2
Are answer keys to multiple-choice tests generated randomly, or are they constructed to make it less likely for the same answer to occur twice in a row? This question was addressed in the article “Seek Whence: Answer Sequences and Their Consequences in Key-Balanced Multiple-Choice Tests” (M.
The 2008 General Social Survey asked a large number of people how much time they spent watching TV each day. The mean number of hours was 2.98 with a standard deviation of 2.66. Assume that in a sample of 40 teenagers, the sample standard deviation of daily TV time is 1.9 hours, and that the
Two weights, each labeled as weighing 100 g, are each weighed several times on the same scale. The results, in units of μg above 100 g, are as follows:Since the same scale was used for both weights, and since both weights are similar, it is reasonable to assume that the variance of
A hypothesis test is to be performed, and it is decided to reject the null hypothesis if P ≤ 0.10. If H0 is in fact true, what is the maximum probability that it will be rejected?
Five new paint additives have been tested to see if any of them can reduce the mean drying time from the current value of 12 minutes. Ten specimens have been painted with each of the new types of paint, and the drying times (in minutes) have been measured. The results are as follows:For each
The article ??n-Nonane Hydroconversion on Ni and Pt Containing HMFI, HMOR and HBEA?? (G. Kinger and H. Vinek, Applied Catalysis A: General, 2002:139??149) presents hydroconversion rates (in μmol/g ? s) of n-nonane over both HMFI and HBEA catalysts. The results are as follows: Can you conclude
In August and September 2005, Hurricanes Katrina and Rita caused extraordinary flooding in New Orleans, Louisiana. Many homes were severely damaged or destroyed; of those that survived, many required extensive cleaning. Itwas thought that cleaning flood-damaged homes might present a health hazard
A certain type of stainless steel powder is supposed to have a mean particle diameter of μ = 15 μm. A random sample of 87 particles had a mean diameter of 15.2 μm, with a standard deviation of 1.8 μm. A test is made of H0 :μ = 15 versus H1 :μ ≠ 15.a. Find the P-value.b. Do you believe it is
A new process for producing a type of novolac resin is supposed to have a mean cycle time of 3.5 hours per batch. Six batches are produced, and their cycle times, in hours, were. ? Can you conclude that the mean cycle time is greater than 3.5 hours? 3.45 3.47 3.57 3.52 3.40 3.63
Two microprocessors are compared on a sample of six benchmark codes to determine whether there is a difference in speed. The times (in seconds) used by each processor on each code are given in the following table.Can you conclude that the mean speeds of the two processors differ? Code 2 3 4 5 6
The article “The Effect of Restricting Opening Hours on Alcohol-Related Violence” (S. Duailibi,W. Ponicki, et al., American Journal of Public Health, 2007:2276–2280) presented homicide rates for the years 1995–2005 for the town of Diadema, Brazil. In 2002, a law was passed requiring bars to
Scores on the math SAT are normally distributed. A sample of 20 SAT scores had standard deviation s = 87. Someone says that the scoring system for the SAT is designed so that the population standard deviation will be σ = 100. Do these data provide sufficient evidence to contradict this claim?
A new process is being considered for the liquefaction of coal. The old process yielded a mean of 15 kg of distillate fuel per kilogram of hydrogen consumed in the process. Let μ represent the mean of the new process. A test of H0 :μ ≤ 15 versus H1 :μ > 15 will be performed. The new
A grinding machine will be qualified for a particular task if it can be shown to produce less than 8% defective parts. In a random sample of 300 parts, 12 were defective. On the basis of these data, can the machine be qualified?
For the given table of observed values,a. Construct the corresponding table of expected values.b. If appropriate, perform the chi-square test for the null hypothesis that the row and column outcomes are independent. If not appropriate, explain why. Observed Values 1 2 25 4 11 B 3 3 42 5
Let μ be the radiation level to which a radiation worker is exposed during the course of a year. The Environmental Protection Agency has set the maximum safe level of exposure at 5 rem per year. If a hypothesis test is to be performed to determine whether a workplace is safe, which is the most
Fifty specimens of a new computer chip were tested for speed in a certain application, along with 50 specimens of chips with the old design. The average speed, in MHz, for the new chips was 495.6, and the standard deviation was 19.4. The average speed for the old chips was 481.2, and the standard
Twenty-one independent measurements were taken of the hardness (on the Rockwell C scale) of HSLA-100 steel base metal, and another 21 independent measurements were made of the hardness of a weld produced on this base metal. The standard deviation of the measurements made on the base metal was 3.06,
One of the ways in which doctors try to determine how long a single dose of pain reliever will provide relief is to measure the drug’s half-life, which is the length of time it takes for one-half of the dose to be eliminated from the body. A report of the National Institutes of Health states that
The article “Effects of Aerosol Species on Atmospheric Visibility in Kaohsiung City, Taiwan” (C. Lee, C. Yuan, and J. Chang, Journal of Air and Waste Management, 2005:1031–1041) reported that for a sample of 20 days in the winter, the mass ratio of fine to coarse particles averaged 0.51 with
Colonoscopy is a medical procedure that is designed to find and remove precancerous lesions in the colon before they become cancerous. The article “Association of Colonoscopy and Death from Colorectal Cancer” (N. Baxter, M. Goldwasser, et al., Annals of Internal Medicine 2009:1–8) reports
In an experiment to determine the effect of curing time on compressive strength of concrete blocks, two samples of 15 blocks each were prepared identically except for curing time. The blocks in one sample were cured for two days, while the blocks in the other were cured for six days. The
Lasers can provide highly accurate measurements of small movements. To determine the accuracy of such a laser, it was used to take 100 measurements of a known quantity. The sample mean error was 25 μm with a standard deviation of 60μm. The laser is properly calibrated if the mean error is μ = 0.
Twenty formulations of a coating are being tested to see if any of them reduce gear wear. For the Bonferroni-adjusted P-value for a formulation to be 0.05, what must the original P-value be?
A new process for producing silicon wafers for integrated circuits is supposed to reduce the proportion of defectives to 10%. A sample of 250 wafers will be tested. Let X represent the number of defectives in the sample. Let p represent the population proportion of defectives produced by the new
The article €œEffect of Granular Subbase Thickness on Airfield Pavement Structural Response€ (K. Gopalakrishnan and M. Thompson, Journal of Materials in Civil Engineering, 2008:331€“342) presents a study of the effect of the subbase thickness (in mm) on the amount of
Fill in the blank: For observed and expected values,i. The row totals in the observed table must be the same as the row totals in the expected table, but the column totals need not be the same.ii. The column totals in the observed table must be the same as the column totals in the expected table,
Find the upper 5% point of F7,20.
The article “Wind-Uplift Capacity of Residential Wood Roof-Sheathing Panels Retrofitted with Insulating Foam Adhesive” (P. Datin, D. Prevatt, and W. Pang, Journal of Architectural Engineering, 2011:144–154) presents a study of the failure pressures of roof panels. A sample of 15 panels
The article “Factors Associated with Exercise Behavior in People with Parkinson Disease” (T. Ellis, J. Cavanaugh, et al., Physical Therapy, 2011:1838–1848) reported a survey of patients with Parkinson’s disease. Of 164 patients who said they exercised regularly, 76 reported falling in the
The article “Approximate Methods for Estimating Hysteretic Energy Demand on Plan-Asymmetric Buildings” (M. Rathhore, A. Chowdhury, and S. Ghosh, Journal of Earthquake Engineering, 2011:99–123) presents a method, based on a modal pushover analysis, of estimating the hysteretic energy demand
A crossover trial is a type of experiment used to compare two drugs. Subjects take one drug for a period of time, then switch to the other. The responses of the subjects are then compared using matched pair methods. In an experiment to compare two pain relievers, seven subjects took one pain
Because of printer failure, none of the observed values in the following table were printed, but some of the marginal totals were. Is it possible to construct the corresponding table of expected values from the information given? If so, construct it. If not, describe the additional information you
The installation of a radon abatement device is recommended in any home where the mean radon concentration is 4.0 picocuries per liter (pCi/L) or more, because it is thought that long-term exposure to sufficiently high doses of radon can increase the risk of cancer. Seventy-five measurements are
In a certain supermarket, a sample of 60 customers who used a self-service checkout lane averaged 5.2 minutes of checkout time, with a standard deviation of 3.1 minutes. A sample of 72 customers who used a cashier averaged 6.1 minutes with a standard deviation of 2.8 minutes.a. Can you conclude
The article ??Modeling of Urban Area Stop-and-Go Traffic Noise?? (P. Pamanikabud and C. Tharasawatipipat, Journal of Transportation Engineering, 1999:152??159) presents measurements of traffic noise, in dBA, from 10 locations in Bangkok, Thailand. Measurements, presented in the following table,
Find the upper 1% point of F2,5.
The article “Association Between Exposure to Emissions from the Oil and Gas Industry and Pathology of the Immune, Nervous, and Respiratory Systems, and Skeletal and Cardiac Muscle in Beef Calves” (C. Waldner and E. Clark, Annals of Environmental and Occupational Health, 2009:6–27) reports
A woman who has moved into a new house is trying to determine which of two routes to work has the shorter average driving time. Times in minutes for six tripson route A and five trips on route B are as follows: Can you conclude that the mean time is less for route A? A: 16.0 15.7 16.4 15.9 16.2
A new concrete mix is being designed to provide adequate compressive strength for concrete blocks. The specification for a particular application calls for the blocks to have a mean compressive strength μ greater than 1350 kPa. A sample of 100 blocks is produced and tested. Their mean compressive
Refer to Exercise 12 in Section 5.3. Can you conclude that the mean penetration resistance is greater than 2.5?Refer to Exercise 12The article “Influence of Penetration Rate on Penetrometer Resistance” (J. Oliveira, M. Almeida, et al., Journal of Geotechnical and Geoenvironmental Engineering,
The following MINITAB output presents the results of a power calculation for a test concerning a population mean μ. a. Is the power calculated for a one-tailed or two-tailed test? b. Assume that the value of μ used for the null hypothesis is μ = 3. For what alternate value of μ is the power
A group of eight individuals with high cholesterol levels were given a new drug that was designed to lower cholesterol levels. Cholesterol levels, in mg/dL, were measured before and after treatment for each individual, with the following results:a. Can you conclude that the mean cholesterol level
A population geneticist is studying the genes found at two different locations on the genome. He estimates the proportion p̂1 of organisms who have gene A at the first locus to be p̂1 = 0.42, with uncertainty σ1 = 0.049. He estimates the proportion of organisms that have gene B at a second locus
The management of a taxi cab company is trying to decide if they should switch from bias tires to radial tires to improve fuel economy. Each of 10 taxis was equipped with one of the two tire types and driven on a test course. Without changing drivers, tires were then switched to the other tire type
A machine that grinds valves is set to produce valves whose lengths have mean 100 mm and standard deviation 0.1 mm. The machine is moved to a new location. It is thought that the move may have upset the calibration for the mean length, but that it is unlikely to have changed the standard deviation.
Fill in the blank: If the null hypothesis is H0 :μ ≤ 5, then the mean of X̅ under the null distribution is.i. 0ii. 5iii. Any number less than or equal to 5.iv. We can’t tell unless we know H1.
Refer to Exercise 13 in Section 5.3. Can you conclude that the mercury content is less than 0.3 ppm?Refer to Exercise 13Ten samples of coal from a Northern Appalachian source had an average mercury content of 0.242 ppm with a standard deviation of 0.031 ppm. Find a 95% confidence for the mean
The following MINITAB output presents the results of a hypothesis test for a population proportion p. a. Is this a one-tailed or two-tailed test? b. What is the null hypothesis? c. Can H0 be rejected at the 2% level? How can you tell? d. Someone asks you whether the null hypothesis H0 : p ?? 0.45
The article €œDetermination of Carboxyhemoglobin Levels and Health Effects on Officers Working at the Istanbul Bosphorus Bridge€ (G. Kocasoy and H. Yalin, Journal of Environmental Science and Health, 2004:1129€“1139) presents assessments of health outcomes of people
The following MINITAB output presents the results of a hypothesis test for the difference μX?? μYbetween two population means. a. Is this a one-tailed or two-tailed test? b. What is the null hypothesis? c. Can H0 be rejected at the 1% level? How can you tell? d. Use the output and an
A machine that fills cereal boxes is supposed to be calibrated so that the mean fill weight is 12 oz. Let μ denote the true mean fill weight. Assume that in a test of the hypotheses H0 :μ = 12 versus H1 :μ = 12, the P-value is 0.30.a. Should H0 be rejected on the basis of this test? Explain.b.
The following MINITAB output presents the results of a hypothesis test for the difference μX?? μYbetween two population means: a. Is this a one-tailed or two-tailed test? b. What is the null hypothesis? c. Can H0 be rejected at the 5% level? How can you tell? d. The output presents a Student??s
A broth used to manufacture a pharmaceutical product has its sugar content, in mg/mL, measured several times on each of three successive days.a. Can you conclude that the variability of the process is greater on the second day than on the first day?b. Can you conclude that the variability of the
Resistors for use in a certain application are supposed to have a mean resistance μ greater than 100 Ω. Assume that the standard deviation of the resistances is 5 Ω. Resistances will be measured for a sample of resistors, and a test of the hypothesis H0 :μ ≤ 100 versus H1 :μ > 100 will be
The article “Variance Reduction Techniques: Experimental Comparison and Analysis for Single Systems” (I. Sabuncuoglu, M. Fadiloglu, and S. Celik, IIE Transactions, 2008:538–551) describes a study of the effectiveness of the method of Latin Hypercube Sampling in reducing the variance of
In a study conducted by the U.S. Department of Health and Human Services, a sample of 546 boys aged 6–11 was weighed, and it was determined that 87 of them were overweight. A sample of 508 girls aged 6–11 was also weighed, and 74 of them were overweight. Can you conclude that the proportion of
Fill in the blank: In a test of H0 :μ ≥ 10 versus H1 :μ < 10, the sample mean was X̅ = 8 and the P-value was 0.04. This means that if μ = 10, and the experiment were repeated 100 times, we would expect to obtain a value of X of 8 or less approximately times.i. 8ii. 0.8iii. 4iv. 0.04v. 80
The following MINITAB output presents the results of a hypothesis test for a population mean μ. a. Is this a one-tailed or two-tailed test? b. What is the null hypothesis? c. Can H0 be rejected at the 1% level? How can you tell? d. Use the output and an appropriate table to compute the P-value
A method of applying zinc plating to steel is supposed to produce a coating whose mean thickness is no greater than 7 microns. A quality inspector measures the thickness of 36 coated specimens and tests H0 : μ ≤ 7 versus H1 : μ > 7. She obtains a P-value of 0.40. Since P > 0.05, she
Refer to Exercise 11 in Section 5.6. Can you conclude that the variance of the sodium content differs between the two brands?Refer to Exercise 11 Brand A 34.36 31.26 37.36 28.52 33.14 32.74 34.34 34.33 30.95 Brand B 41.08 38.22 39.59 38.82 36.24 37.73 35.03 39.22 34.13 34.33 34.98 29.64 40.60
In order to determine whether to pitch a new advertising campaign more toward men or women, an advertiser provided each couple in a random sample of 500 married couples with a new type of TV remote control that is supposed to be easier to find when needed. Of the 500 husbands, 62% said that the new
Refer to Exercise 14. Someone wants to compute a 95% confidence interval for the mean runoff when the rainfall is 3 in. Can this be computed from the information in the MINITAB output shown in Exercise 14? Or is more information needed? Choose the best answer.i. Yes, it can be computed from the
Refer to Exercise 1. If 95% confidence intervals are constructed for the yield of the reaction at temperatures of 45°C, 60°C, and 75°C, which confidence interval would be the shortest? Which would be the longest?
The article €œEffect of Environmental Factors on Steel Plate Corrosion Under Marine Immersion Conditions€ (C. Soares, Y. Garbatov, and A. Zayed, Corrosion Engineering, Science and Technology, 2011:524€“ 541) describes an experiment in which nine steel specimens were
Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article ??Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network?? (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863??872)
Deforestation is a serious problem throughout much of India. The article ??Factors Influencing People??s Participation in Forest Management in India?? (W. Lise, Ecological Economics, 2000:379??392) discusses the social forces that influence forest management policies in three Indian states:
Anthropologists can estimate the birthrate of an ancient society by studying the age distribution of skeletons found in ancient cemeteries. The numbers of skeletons found at two such sites, as reported in the article ??Paleoanthropological Traces of a Neolithic Demographic Transition?? (J.
Two machines are used to package laundry detergent. It is known that weights of boxes are normally distributed. Four boxes from each machine have their contents carefully weighed, with the following results (in grams): An engineer wishes to test the null hypothesis that the mean weights of boxes
Suppose the Environmental Protection Agency is in the process of monitoring the water quality in a large estuary in the eastern United States, in order to measure the PCB concentration (in parts per billion). a. Suppose that a random sample of size 80 has a sample mean of 1.59 ppb and a sample
Refer to Exercise 18. It is discovered that the standard deviation of the sample used to compute the confidence interval is 5 N. Is it possible to determine whether P < 0.01? Explain.Refer to Exercise 18.A shipment of fibers is not acceptable if the mean breaking strength of the fibers is less
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