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Statistics For Engineers And Scientists 3rd Edition William Navidi - Solutions
A tire manufacturer is interested in testing the fuel economy for two different tread patterns. Tires of each tread type are driven for 1000 miles on each of 18 different cars. The mileages, in mpg, are presented in the following table.a. Find a 99% confidence interval for the mean difference in
A sample of 25 resistors, each labeled 100(, had an average resistance of 101.4( with a standard deviation of 2.3(. Assume the resistances are normally distributed. a. Find a 95% prediction interval for the resistance of a single resistor. b. Find a tolerance interval for the resistance that
The article "Ozone for Removal of Acute Toxicity from Logyard Run-off" (M. Zenaitis and S. Duff, Ozone Science and Engineering, 2002: 83-90) presents chemical analyses of runoff water from sawmills in British Columbia. Included were measurements of pH for six water specimens: 5.9, 5.0, 6.5, 5.6,
Five measurements are taken of the octane rating for a particular type of gasoline. The results (in percent) are 87.0, 86.0, 86.5, 88.0, 85. 3. a. Find a 95% prediction interval for a single measurement. b. Find a tolerance interval for the pH that includes 90% of the measurements with 99%
In the article "Occurrence and Distribution of Ammonium in Iowa Groundwater" (K. Schilling, Water Environment Research, 2002:177-186), ammonium concentrations (in mg/L) were measured at a large number of wells in the state of Iowa. These included 349 alluvial wells and 143 quaternary wells. The
This exercise is designed to compare the performance of the Agresti-Coull confidence interval for a proportion (expression 5.5 on page 339) with that of the traditional confidence interval (expression 5.8 on page 341). We will use sample sizes of n = 10, n = 17, and n = 40, with p = 0.5. a.
A molecular biologist is studying the effectiveness of a particular enzyme to digest a certain sequence of DNA nucleotides. He divides six DNA samples into two parts, treats one part with the enzyme, and leaves the other part untreated. He then uses a polymerase chain reaction assay to count the
In the article "Groundwater Electromagnetic Imaging in Complex Geological and Topographical Regions: A Case Study of a Tectonic Boundary in the French Alps" (S. Houtot, P. Tarits, et al., Geophysics, 2002:1048-1060), the pH was measured for several water samples in various locations near Gittaz
A 99% confidence interval for a population mean based on a sample of size 64 is computed to be (16.3, 18.7). How large a sample is needed so that a 99% confidence interval will specify the mean to within ±1.0?
A metallurgist makes several measurements of the melting temperature of a certain alloy and computes a 95% confidence interval to be 2038±2◦C. Assume the measuring process for temperature is unbiased. True or false: a. There is 95% probability that the true melting temperature is in the interval
The temperature of a certain solution is estimated by taking a large number of independent measurements and averaging them. The estimate is 37◦C, and the uncertainty (standard deviation) in this estimate is 0.1◦C. a. Find a 95% confidence interval for the temperature. b. What is the confidence
Let X represent the number of events that are observed to occur in n units of time or space, and assume X ∼ Poisson(nλ), where λ is the mean number of events that occur in one unit of time or space. Assume X is large, so that X ∼ N(nλ, nλ). Follow steps (a) through (d) to derive a level
In a Couette flow, two large flat plates lie one atop another, separated by a thin layer of fluid. If a shear stress is applied to the top plate, the viscosity of the fluid produces motion in the bottom plate as well. The velocity V in the top plate relative to the bottom plate is given by V =
The article "Genetically Based Tolerance to Endosulfan, Chromium (VI) and Fluoranthene in the Grass Shrimp Palaemonetes pugio" (R. Harper- Arabie, Ph.D. Thesis, Colorado School of Mines, 2002) reported that out of 1985 eggs produced by shrimp at the Diesel Creek site in Charleston, South Carolina,
A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N. A new batch of yarnwas made, using newrawmaterials from a different vendor. In a sample of 75 pieces of yarn from the new batch, the mean breaking strength was 5.8 N and the standard deviation was 1.0 N.
Leakage from underground fuel tanks has been a source of water pollution. In a random sample of 87 gasoline stations, 13 were found to have at least one leaking underground tank. a. Find a 95% confidence interval for the proportion of gasoline stations with at least one leaking underground tank. b.
Three confidence intervals for the mean shear strength (in ksi) of anchor bolts of a certain type are computed, all from the same sample. The intervals are (4.01, 6.02), (4.20, 5.83), and (3.57, 6.46). The levels of the intervals are 90%, 95%, and 99%. Which interval has which level?
In an experiment to measure the lifetimes of parts manufactured from a certain aluminum alloy, 73 parts were loaded cyclically until failure. The mean number of kilocycles to failure was 783, and the standard deviation was 120. Let μ represent the mean number of kilocycles to failure for parts of
An engineer takes a large number of independent measurements of the length of a component and obtains X̅ = 5.2 mm and σX̅ = 0.1 mm. Use this information to find the P-value for testing H0 :μ = 5.0 versus H1 :μ = 5.0?
The following MINITAB output presents the results of a hypothesis test for a population mean μ. Some of the numbers are missing. Fill in the numbers for (a) through (c).
The article "Evaluation of Mobile Mapping Systems for Roadway Data Collection" (H. Karimi, A. Khattak, and J. Hummer, Journal of Computing in Civil Engineering, 2000:168-173) describes a system for remotely measuring roadway elements such as the width of lanes and the heights of traffic signs. For
Recently many companies have been experimenting with telecommuting, allowing employees to work at home on their computers. Among other things, telecommuting is supposed to reduce the number of sick days taken. Suppose that at one firm, it is known that over the past few years employees have taken a
When it is operating properly, a chemical plant has a mean daily production of at least 740 tons. The output is measured on a simple random sample of 60 days. The sample had a mean of 715 tons/day and a standard deviation of 24 tons/day. Let μ represent the mean daily output of the plant. An
The article "Predicting Profit Performance for Selecting Candidate International Construction Projects" (S. Han, D. Kim, and H. Kim, Journal of Construction Engineering and Management Science, 2007: 425-436) presents an analysis of the profit of international construction projects. In a sample of
Fasteners are manufactured for an application involving aircraft. Each fastener is categorized either as conforming (suitable for its intended use), downgraded (unsuitable for its intended use but usable for another purpose), and scrap (not usable). It is thought that 85% of the fasteners are
Plates are evaluated according to their surface finish, and placed into four categories: premium, conforming, downgraded, and unacceptable. A quality engineer claims that the proportions of plates in the four categories are 10%, 70%, 15%, and 5%, respectively. In a sample of 200 plates, 19 were
The article "Analysis of Unwanted Fire Alarm: Case Study" (W. Chow, N. Fong, and C. Ho, Journal of Architectural Engineering, 1999:62-65) presents a count of the number of false alarms at several sites. The numbers of false alarms each month, divided into those with known causes and those with
The article "Inconsistent Health Perceptions for US Women and Men with Diabetes" (M. McCollum, L. Hansen, et al., Journal of Women's Health, 2007:1421-1428) presents results of a survey of adults with diabetes. Each respondent was categorized by gender and income level. The numbers in each category
The article "Chronic Beryllium Disease and Sensitization at a Beryllium Processing Facility" (K. Rosenman, V. Hertzberg, et al., Environmental Health Perspectives, 2005:1366-1372) discusses the effects of exposure to beryllium in a cohort ofworkers. Workers were categorized by their duration of
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.
An F test with five degrees of freedom in the numerator and seven degrees of freedom in the denominator produced a test statistic whose value was 7.46. a. What is the P-value if the test is one-tailed? b. What is the P-value if the test is two-tailed?
Refer to Exercise 11 in Section 5.6. Can you conclude that the variance of the breaking strengths differs between the two composites?
A hypothesis test is performed, and the P-value is 0.03. True or false: a. H0 is rejected at the 5% level. b. H0 is rejected at the 2% level. c. H0 is not rejected at the 10% level?
A new braking system is being evaluated for a certain type of car. The braking system will be installed if it can be conclusively demonstrated that the stopping distance under certain controlled conditions at a speed of 30 mi/h is less than 90 ft. It is known that under these conditions the
A vendor claims that no more than 10% of the parts she supplies are defective. Let p denote the actual proportion of parts that are defective. A test is made of the hypotheses H0 : p ≤ 0.10 versus H1 : p > 0.10. For each of the following situations, determine whether the decision was correct, a
A test has power 0.90 when μ = 15. True or false: a. The probability of rejecting H0 when μ = 15 is 0.90. b. The probability of making a correct decision when μ = 15 is 0.90. c. The probability of making a correct decision when μ = 15 is 0.10. d. The probability that H0 is true when μ = 15 is
The following MINITAB output presents the results of a power calculation for a test of the difference between two means μ1 μ2.a. Is the power calculated for a one-tailed or two-tailed test? b. If the sample sizes were 50 in each group, would the power be
A tire company claims that the lifetimes of its tires average 50,000 miles. The standard deviation of tire lifetimes is known to be 5000 miles. You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50,000 miles against the alternative that it is less. Assume, in
A power calculation has shown that if μ = 8, the power of a test of H0 :μ ≥ 10 versus H1 :μ < 10 is 0.90. If instead μ = 7, which one of the following statements is true? (i) The power of the test will be less than 0.90. (ii) The power of the test will be greater than 0.90. (iii) We cannot
The following MINITAB output presents the results of a power calculation for a test concerning a population proportion p.a. Is the power calculated for a one-tailed or two-tailed test? b. What is the null hypothesis for which the power is calculated? c. For what alternative value of p is the power
Six different settings are tried on a machine to see if any of them will reduce the proportion of defective parts. For each setting, an appropriate null hypothesis is tested to see if the proportion of defective parts has been reduced. The six P-values are 0.34, 0.27, 0.002, 0.45, 0.03, and
Each day for 200 days, a quality engineer samples 144 fuses rated at 15 A and measures the amperage at which they burn out. He performs a hypothesis test of H0 :μ = 15 versus H1 :μ ( 15, where μ is the mean burnout amperage of the fuses manufactured that day. a. On 10 of the 200 days, H0 is
This exercise continues Exercise 9 in the Supplementary Exercises for Chapter 3. The article "Insights into Present-Day Crustal Motion in the Central Mediterranean Area from GPS Surveys" (M. Anzidei, P. Baldi, et al., Geophysical Journal International, 2001:98-100) reports measurements of the
Refer to Exercise 6 in Section 5.9. Let μ represent the population mean compressive strength, in MPa. Consider the following null hypotheses: i. H0 : μ = 38.53 ii. H0 : μ = 38.35 iii. H0 : μ = 38.45 iv. H0 : μ = 38.55 a. Using the bootstrap data presented in Exercise 6 in Section 5.9, which of
For the lettuce yield data, (page 494) it is thought that the yields from fertilizer A might have a larger variance than the yields from fertilizer B. a. Compute the sample variances s2A and s2B of the yields assigned to A and B, respectively, and the quotient s2A/s2B. b. Someone suggests using the
A certain wastewater treatment method is supposed to neutralize the wastewater so that the mean pH is 7. Measurements of pH will be made on seven specimens of treated wastewater, and a test of the hypotheses H0 :μ = 7 versus H1 :μ ( 7 will be made using the Student's t test (Section 6.4). Assume
It is desired to check the calibration of a scale by weighing a standard 10 g weight 100 times. Let μ be the population mean reading on the scale, so that the scale is in calibration if μ = 10. A test is made of the hypotheses H0 :μ = 10 versus H1 :μ ( 10. Consider three possible conclusions:
The strength of a certain type of rubber is tested by subjecting pieces of the rubber to an abrasion test. For the rubber to be acceptable, the mean weight loss μ must be less than 3.5 mg. A large number of pieces of rubber that were cured in a certain way were subject to the abrasion test. A 95%
Refer to Exercise 17. It is discovered that the mean of the sample used to compute the confidence bound is X̅ = 3.40. Is it possible to determine whether P < 0.01? Explain.
True or false: If P = 0.02, then a. The result is statistically significant at the5%level. b. The result is statistically significant at the1%level. c. The null hypothesis is rejected at the 5% level. d. The null hypothesis is rejected at the 1% level.
In each of the following situations, state the most appropriate null hypothesis regarding the population mean μ. a. A new type of battery will be installed in heart pacemakers if it can be shown to have a mean lifetime greater than eight years. b. A new material for manufacturing tires will be
A random sample of 300 electronic components manufactured by a certain process are tested, and 25 are found to be defective. Let p represent the proportion of components manufactured by this process that are defective. The process engineer claims that p ≤ 0.05. Does the sample provide enough
Refer to Exercise 2 in Section 5.2. Can it be concluded that more than 60% of the residences in the town reduced their water consumption?
The following MINITAB output presents the results of a hypothesis test for a population proportion p. Some of the numbers are missing. Fill in the numbers for (a) through (c)?
Do bathroom scales tend to underestimate a person's true weight? A 150 lb test weight was placed on each of 50 bathroom scales. The readings on 29 of the scales were too light, and the readings on the other 21 were too heavy. Can you conclude that more than half of bathroom scales underestimate
In a survey of 500 residents in a certain town, 274 said they were opposed to constructing a new shopping mall. Can you conclude that more than half of the residents in this town are opposed to constructing a new shopping mall?
In a sample of 150 households in a certain city, 110 had high-speed internet access. Can you conclude that more than 70% of the households in this city have high-speed internet access?
Let A and B represent two variants (alleles) of the DNA at a certain locus on the genome. Assume that 40% of all the alleles in a certain population are type A and 30% are type B. The locus is said to be in Hardy- Weinberg equilibrium if the proportion of organisms that are of type AB is (0.40)
Each of the following hypothetical data sets represents some repeated weighings of a standard weight that is known to have a mass of 100 g. Assume that the readings are a random sample from a population that follows the normal curve. Perform a t test to see whether the scale is properly calibrated,
Refer to Exercise 13 in Section 5.3. Can you conclude that the lead concentration is less than 14μg/L?
The following MINITAB output presents the results of a hypothesis test for a population mean μ. Some of the numbers are missing. Fill them in.
A new process for synthesizing methanol from methane is under study to evaluate its technical feasibility. Design simulations indicate that the reactor must have a mean methane conversion greater than 35% for the process to be feasible. In an initial study, six runs were made. The average
The article "Effect 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 on the amount of surface deflection caused by aircraft
Specifications call for the wall thickness of two-liter polycarbonate bottles to average 4.0 mils. A quality control engineer samples 7 two-liter polycarbonate bottles from a large batch and measures the wall thickness (in mils) in each. The results are: 3.999, 4.037, 4.116, 4.063, 3.969, 3.955,
The article "Variance Reduction Techniques: Experimental Comparison and Analysis for Single Systems" (I. Sabuncuoglu, M. Fadiloglu, and S. IIE Transactions, 2008:538-551) describes a study of methods for reducing variance in estimators of the mean inventory on hand for a standard inventory model.
The article "Capillary Leak Syndrome in Children With C4A-Deficiency Undergoing Cardiac Surgery With Cardiopulmonary Bypass: A Double-Blind, Randomised Controlled Study" (S. Zhang, S. Wang, et al., Lancet, 2005:556-562) presents the results of a study of the effectiveness of giving blood plasma
The National Opinion Research Center polled a sample of 92 people aged 18-22 in the year 2002, asking them how many hours per week they spent on the internet. The sample mean was 7.38, with a sample standard deviation of 12.83. A second sample of 123 people aged 18-22 was taken in the year 2004.
The following MINITAB output presents the results of a hypothesis test for the difference μX μY between two population means. Some of the numbers are missing.a. Fill in the missing numbers for (i) and (ii). b. The output presents a Student's t test. Compute
The article "Some Parameters of the Population Biology of Spotted Flounder (Ciutharus linguatula Linnaeus, 1758) in Edremit Bay (North Aegean Sea)," (D.T¨urker, B. Bayhan, et al., Turkish Journal of Veterinary and Animal Science, 2005:1013-1018) reports that a sample of 482 female spotted flounder
In a test to compare the effectiveness of two drugs designed to lower cholesterol levels, 75 randomly selected patients were given drug A and 100 randomly selected patients were given drug B. Those given drug A reduced their cholesterol levels by an average of 40 with a standard deviation of 12,
A statistics instructor who teaches a lecture section of 160 students wants to determine whether students have more difficulty with one-tailed hypothesis tests or with two-tailed hypothesis tests. On the next exam, 80 of the students, chosen at random, get a version of the exam with a 10-point
Are low-fat diets or low-carb diets more effective for weight loss? This question was addressed in the article "Comparison of the Atkins, Zone, Ornish, and LEARN Diets for Change in Weight and Related Risk Factors Among Overweight Premenopausal Women: The ATOZ Weight Loss Study: A Randomized Trial"
Two extrusion machines that manufacture steel rods are being compared. In a sample of 1000 rods taken from machine 1, 960 met specifications regarding length and diameter. In a sample of 600 rods taken from machine 2, 582 met the specifications. Machine 2 is more expensive to run, so it is decided
The article "Long-term Outcomes of Patients Receiving Drug-eluting Stents" (A. Philpott, D. Southern, et al., Canadian Medical Association Journal, 2009:167-174) reported that in a sample of 5320 angioplasty patients receiving bare metal stents, 195 died within one year, and in a sample of 1120
The following MINITAB output presents the results of a hypothesis test for the difference p1 p2 between two population proportions. Some of the numbers are missing. Fill in the numbers for (a) through (d).
The article "Strategic Management in Engineering Organizations" (P. Chinowsky, Journal of Management in Engineering, 2001:60-68) presents results of a survey on management styles that was administered both to private construction firms and to public agencies. Out of a total of 400 private firms
The article "HIV-positive Smokers Considering Quitting: Differences by Race/Ethnicity" (E. Lloyd- Richardson, C. Stanton, et al., Am J Health Behav, 2008:3-15) reported that in a group of 230 European- American HIV-positive smokers, 102 of them had used a nicotine patch to try to quit smoking, and
To test the effectiveness of protective packaging, a firm shipped out 1200 orders in regular light packaging and 1500 orders in heavy-duty packaging. Of the orders shipped in light packaging, 20 arrived in damaged condition, while of the orders shipped in heavyduty packaging, 15 arrived in damaged
In the article "Nitrate Contamination of Alluvial Groundwaters in the Nakdong River Basin, Korea" (J. Min, S. Yun, et al., Geosciences Journal, 2002: 35-46), 41 water samples taken from wells in the Daesan area were described, and 22 of these were found to meet quality standards for drinking water.
A crayon manufacturer is comparing the effects of two kinds of yellow dye on the brittleness of crayons. Dye B is more expensive than dye A, but it is thought that it might produce a stronger crayon. Four crayons are tested with each kind of dye, and the impact strength (in joules) is measured for
The article "Structural Performance of Rounded Dovetail Connections Under Different Loading Conditions" (T. Tannert, H. Prion, and F. Lam, Can J Civ Eng, 2007:1600-1605) describes a study of the deformation properties of dovetail joints. In one experiment, 10 rounded dovetail connections and 10
In an experiment to test the effectiveness of a new sleeping aid, a sample of 12 patients took the new drug, and a sample of 14 patients took a commonly used drug. Of the patients taking the new drug, the average time to fall asleep was 27.3 minutes with a standard deviation of 5.2 minutes, and for
Refer to Exercise 12 in Section 5.6. Can you conclude that the mean permeability coefficient at 60◦C differs from that at 61◦C?
The following MINITAB output presents the results of a hypothesis test for the difference μX μY between two population means. Some of the numbers are missing. Fill in the numbers for (a) through (d).
The article "Modeling Resilient Modulus and Temperature Correction for Saudi Roads" (H. Wahhab, I. Asi, and R. Ramadhan, Journal of Materials in Civil Engineering, 2001:298-305) describes a study designed to predict the resilient modulus of pavement from physical properties. One of the questions
The article "Calibration of an FTIR Spectrometer" (P. Pankratz, Statistical Case Studies for Industrial and Process Improvement, SIAM-ASA, 1997:19-38) describes the use of a spectrometer to make five measurements of the carbon content (in ppm) of a certain silicon wafer on each of two successive
It is thought that a new process for producing a certain chemical may be cheaper than the currently used process. Each process was run 6 times, and the cost of producing 100 L of the chemical was determined each time. The results, in dollars, were as follows:Can you conclude that the mean cost of
The article "Mechanical Grading of Oak Timbers" (D. Kretschmann and D. Green, Journal of Materials in Civil Engineering, 1999:91-97) presents measurements of the ultimate compressive stress, in MPa, for green mixed oak 7 by 9 timbers from West Virginia and Pennsylvania. For 11 specimens of no. 1
Muscles flex when stimulated through electric impulses either to motor points (points on the muscle) or to nerves. The article "Force Assessment of the Stimulated Arm Flexors: Quantification of Contractile Properties" (J. Hong and P. Iaizzo, Journal of Medical Engineering and Technology,
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
The following MINITAB output presents the results of a hypothesis test for the difference μX μY between two population means. Some of the numbers are missing. Fill in the numbers for (a) through (d).
A dry etch process is used to etch silicon dioxide (SiO2) off of silicon wafers. An engineer wishes to study the uniformity of the etching across the surface of the wafer. A total of 10 wafers are sampled after etching, and the etch rates (in A ¦ /min) are measured at two different
Two formulations of a certain coating, designed to inhibit corrosion, are being tested. For each of eight pipes, half the pipe is coated with formulation A and the other half is coated with formulation B. Each pipe is exposed to a salt environment for 500 hours. Afterward, the corrosion loss (in
The compressive strength, in kilopascals, was measured for concrete blocks from five different batches of concrete, both three and six days after pouring. The data are presented in the following table.Can you conclude that the mean strength after six days is greater than the mean strength after
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
The article "Wastewater Treatment Sludge as a Raw Material for the Production of Bacillus thuringiensis Based Biopesticides" (M. Tirado Montiel, R. Tyagi, and J. Valero, Water Research, 2001: 3807-3816) presents measurements of total solids, in g/L, for seven sludge specimens. The results (rounded
This exercise shows that the signed-rank test can be used with paired data. Two gauges that measure tire tread depth are being compared. Ten different locations on a tire are measured once by each gauge. The results, in mm, are presented in the following table.Assume the differences are a sample
A new postsurgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven others (the controls) receive the standard treatment. The recovery times, in days, are as follows:Can you conclude that the mean rate differs between the treatment and
In a comparison of the effectiveness of distance learning with traditional classroom instruction, 12 students took a business administration course online, while 14 students took it in a classroom. The final exam scores were as follows.Can you conclude that the mean score differs between the two
A fleet of 100 taxis is divided into two groups of 50 cars each to see whether premium gasoline reduces maintenance costs. Premium unleaded fuel is used in group A, while regular unleaded fuel is used in group B. The total maintenance cost for each vehicle during a one-year period is recorded.
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