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statistics

Questions and Answers of Statistics

A machine that grinds valves is set to produce valves whose lengths have mean 100mmand standard deviation 0.1 mm. The machine is moved to a new location. It is thought that the move may have upset
A machine manufactures bolts that are supposed to be 3 inches in length. Each day a quality engineer selects a random sample of 50 bolts from the day's production, measures their lengths, and
Refer to Exercise 14. The process engineer notices that the sample from line 3 has the lowest proportion of failures. Use the Bonferroni adjustment to determine whether she can conclude that the
The rank-sum test is sometimes thought of as a test for population medians. Under the assumptions of equal spread and shape, the means of two populations will differ if and only if the medians
Two different chemical formulations of rocket fuel are considered for the peak thrust they deliver in a particular design for a rocket engine. The thrust/weight ratios (in kilograms force per gram)
The article "Valuing Watershed Quality Improvements Using Conjoint Analysis" (S. Farber and B. Griner, Ecological Economics, 2000:63-76) presents the results of a mail survey designed to assess
A new quality-inspection program is being tested to see if it will reduce the proportion of parts shipped out that are defective. Under the old program, the proportion of defective parts was 0.10.
Suppose you have purchased a filling machine for candy bags that is supposed to fill each bag with 16 oz of candy. Assume that the weights of filled bags are approximately normally distributed. A
An automobile manufacturer wishes to compare the lifetimes of two brands of tire. She obtains samples of six tires of each brand. On each of six cars, she mounts one tire of each brand on each front
There is concern that increased industrialization may be increasing the mineral content of river water. Ten years ago, the silicon content of the water in a certain river was 5 mg/L. Eighty-five
Compute the correlation coefficient for the following data set.
The article "Drift in Posturography Systems EquippedWith a Piezoelectric Force Platform: Analysis and Numerical Compensation" (L. Quagliarella, N. Sasanelli, and V. Monaco, IEEE Transactions on
The article "'Little Ice Age' Proxy Glacier Mall Balance Records Reconstructed from Tree Rings in the Mt. Waddington Area, British Columbia Coast Mountains, Canada" (S Larocque and D. Smith, The
For each of the following scatterplots, state whether the correlation coefficient is an appropriate summary, and explain briefly.(a)(b) (c)
An investigator collected data on heights and weights of college students. The correlation between height and weight for men was about 0.6, and for women it was about the same. If men and women are
A chemical engineer is studying the effect of temperature and stirring rate on the yield of a certain product. The process is run 16 times, at the settings indicated in the following table. The units
Tire pressure (in kPa) was measured for the right and left front tires on a sample of 10 automobiles. Assume that the tire pressures follow a bivariate normal distribution. Right Tire Left
Each month for several months, the average temperature in ◦C (x) and the number of pounds of steam (y) consumed by a certain chemical plant were measured. The least-squares line computed from the
An agricultural scientist planted alfalfa on several plots of land, identical except for the soil pH. Following are the dry matter yields (in pounds per acre) for each plot. pH
Varying amounts of pectin were added to canned jellies, to study the relationship between pectin concentration in % (x) and a firmness index (y). The means and standard deviations of the x and y
A simple random sample of 100 men aged 25-34 averaged 70 inches in height, and had a standard deviation of 3 inches. Their incomes averaged $34,900 and had a standard deviation of $17,200. Fill in
In Galton's height data (Figure 7.1, in Section 7.1), the least-squares line for predicting forearm length (y) from height (x) is y = −0.2967 + 0.2738x. a. Predict the forearm length of a man whose
Moisture content in percent by volume (x) and conductivity in mS/m (y) were measured for 50 soil specimens. The means and standard deviations were = 8.1, sx = 1.2, = 30.4, sy = 1.9. The
The article "Testing the Influence of Climate, Human Impact and Fire on the Holocene Population Expansion of Fagus sylvatica in the Southern Prealps (Italy)" (V. Valsecchi, W. Flnsinger, et al., The
A chemical reaction is run 12 times, and the temperature xi (in —¦C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are
In the weld data (Example 7.17) imagine that 95% confidence intervals are computed for the mean strength of welds with oxygen contents of 1.3, 1.5, and 1.8 parts per thousand. Which of the confidence
In the following MINITAB output, some of the numbers have been accidentally erased. Recompute them, using the numbers still available. There are n = 25 points in the data set.
In order to increase the production of gas wells, a procedure known as "fracture treatment" is often used. Fracture fluid, which consists of fluid mixed with sand, is pumped into the well. The
Ozone (O3) is a major component of air pollution in many cities. Atmospheric ozone levels are influenced by many factors, including weather. In one study, the mean percent relative humidity (x) and
Refer to Exercises 3 and 4. An atmospheric scientist notices that the slope of the least-squares line in the study described in Exercise 4 differs from the one in the study described in Exercise 3.
The coefficient of absorption (COA) for a clay brick is the ratio of the amount of cold water to the amount of boiling water that the brick will absorb. The article "Effects of Waste Glass Additions
In a study to determine the relationship between ambient outdoor temperature and the rate of evaporation of water from soil, measurements of average daytime temperature in —¦C and
The following output (from MINITAB) is for the least-squares fit of the model ln y = Î²0 + Î²1 ln x + Îµ, where y represents the monthly production of a gas well and
The article "The Equilibrium Partitioning of Titanium Between Ti3+ and Ti4+ Valency States in CaO-SiO2-TiOx Slags" (G. Tranell, O. Ostrovski, and S. Jahanshahi, Metallurgical and Materials
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
To determine the effect of temperature on the yield of a certain chemical process, the process is run 24 times at various temperatures. The temperature (in —¦C) and the yield (expressed
Good forecasting and control of preconstruction activities leads to more efficient use of time and resources in highway construction projects. Data on construction costs (in $1000s) and person-hours
The National Assessment for Educational Progress measured the percentage of eighth grade students who were proficient in reading and the percentage of students who graduated from high school in each
A windmill is used to generate direct current. Data are collected on 45 different days to determine the relationship between wind speed in mi/h (x) and current in kA (y). The data are presented in
The Beer-Lambert law relates the absorbance A of a solution to the concentration C of a species in solution by A = MLC, where L is the path length and M is the molar absorption coefficient. Assume
The article "Estimating Population Abundance in Plant Species with Dormant Life-Stages: Fire and the Endangered Plant Grevillea caleye R. Br." (T. Auld and J. Scott, Ecological Management and
Monitoring the yield of a particular chemical reaction at various reaction vessel temperatures produces the results shown in the following table.a. Find the least-squares estimates for
The article "Low-Temperature Heat Capacity and Thermodynamic Properties of 1,1,1-trifluoro-2,2-dichloroethane" (R. Varushchenko and A. Druzhinina, Fluid Phase Equilibria, 2002:109-119) describes an
Consider the model y = βx + ε, where the intercept of the line is known to be zero. Assume that values (x1, y1) , . . . , (xn, yn) are observed, and the least-squares estimate β of β is to be
Use Equation (7.35) (page 541) to show that Î¼Î²0 = Î²0.
Use Equation (7.35) (page 541) to derive the formulaEquation (7.35)
Eruptions of the Old Faithful geyser in Yellowstone National Park typically last from 1.5 to 5 minutes. Between eruptions are dormant periods, which typically last from 50 to 100 minutes. A dormant
A chemist is calibrating a spectrophotometer that will be used to measure the concentration of carbon monoxide (CO) in atmospheric samples. To check the calibration, samples of known concentration
The article "A Robust Optimization Approach for the Capacitated Vehicle Routing Problem With Demand Uncertainty" (I. Sungur, F. Ordonez, and M. Dessouky, IIE Transactions, 2008:509-523) discusses
The article "Copper Oxide Mounted on Activated Carbon as Catalyst for Wet Air Oxidation of Aqueous Phenol. 1. Kinetic and Mechanistic Approaches" (P. Alvarez, D. McLurgh, and P. Plucinski, Industrial
In an experiment to determine the factors affecting tensile strength in steel plates, the tensile strength (in kg/mm2), the manganese content (in parts per thousand), and the thickness (in mm) were
The following MINITAB output is for a multiple regression. Something went wrong with the printer, so some of the numbers are missing. Fill in the missing numbers.
The article "Evaluating Vent Manifold Inerting Requirements: Flash Point Modeling for Organic Acid-Water Mixtures" (R. Garland and M. Malcolm, Process Safety Progress, 2002:254-260) presents a model
The following data were collected in an experiment to study the relationship between extrusion pressure (in KPa) and wear (in mg).The least-squares quadratic model is y = ˆ’32.445714 +
The November 24, 2001, issue of The Economist published economic data for 15 industrialized nations. Included were the percent changes in gross domestic product (GDP), industrial production (IP),
In an experiment to estimate the acceleration of an object down an inclined plane, the object is released and its distance in meters (y) from the top of the plane is measured every 0.1 second from
The data used to fit the model in Exercise 1 are presented in the following table, along with the residuals and the fitted values. Plot the residuals versus the fitted values. Does the plot indicate
In the article "Application of Statistical Design in the Leaching Study of Low-Grade Manganese Ore Using Aqueous Sulfur Dioxide" (P. Naik, L. Sukla, and S. Das, Separation Science and Technology,
In a study of the lung function of children, the volume of air exhaled under force in one second is called FEV1. (FEV1 stands for forced expiratory volume in one second.) Measurements were made on a
The article "Drying of Pulps in Sprouted Bed: Effect of Composition on Dryer Performance" (M. Medeiros, S. Rocha, et al., Drying Technology, 2002:865-881) presents measurements of pH, viscosity (in
In an experiment to determine factors related to weld toughness, the Charpy V-notch impact toughness in ft · lb (y) was measured for 22 welds at 0—¦C, along with the lateral
Two chemical engineers, A and B, are working independently to develop a model to predict the viscosity of a product (y) from the pH (x1) and the concentration of a certain catalyst (x2). Each
Refer to Exercise 10 in Section 7.4. a. Divide the data into two groups: points where R1 < 4 in one group, points where R1 ≥ 4 in the other. Compute the least-squares line for predicting R2 from R1
True or false: a. For any set of data, there is always one best model. b. When there is no physical theory to specify a model, there is usually no best model, but many that are about equally good. c.
In a study of the causes of bearing wear, a machine was run 24 times, with various loads (denoted x1), oil viscosities (x2), and ambient temperatures (x3). The wear, denoted y, was modeled as y = β0
The article "Ultimate Load Analysis of Plate Reinforced Concrete Beams" (N. Subedi and P. Baglin, Engineering Structures, 2001:1068-1079) presents theoretical and measured ultimate strengths (in kN)
The article "Vehicle-Arrival Characteristics at Urban Uncontrolled Intersections" (V. Rengaraju and V. Rao, Journal of Transportation Engineering, 1995:317-323) presents data on traffic
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
To try to improve the prediction of FEV1, additional independent variables are included in the model. These new variables are Weight (in kg), the product (interaction) of Height and Weight, and the
The article "Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds" (D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s-136s) reports an
The data presented in the following table give the tensile strength in psi (y) of paper as a function of the percentage of hardwood content (x).a. Fit polynomial models of degrees 1, 2, and so on to
A paint company collects data on the durability of its paint and that of its competitors. They measured the lifetimes of three samples of each type of paint in several American cities. The results
The article "Measurements of the Thermal Conductivity and Thermal Diffusivity of Polymer Melts with the Short- Hot-Wire Method" (X. Zhang, W. Hendro, et al., International Journal of Thermophysics,
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,
The article "Lead Dissolution from Lead Smelter Slags Using Magnesium Chloride Solutions" (A. Xenidis, T. Lillis, and I. Hallikia, The AusIMM Proceedings, 1999:37-44) discusses an investigation of
The article "Estimating Resource Requirements at Conceptual Design Stage Using Neural Networks" (A. Elazouni, I. Nosair, et al., Journal of Computing in Civil Engineering, 1997:217-223) suggests that
The following MINITAB output is for a multiple regression. Some of the numbers got smudged, becoming illegible. Fill in the missing numbers.
In a simulation of 30 mobile computer networks, the average speed, pause time, and number of neighbors were measured. A "neighbor" is a computer within the transmission range of another. The data are
In a study to predict temperature from air pressure in a piston-cylinder device, 19 measurements were made of temperature in —¦f (y) and air pressure in psi (x). three models were fit:
Refer to Exercise 2 in Section 8.2. a. Using each of the three models in turn, predict the NOx emission when Speed = 1500, Torque = 400, and HP = 150. b. Using each of the three models in turn,
A study is made of the effect of curing temperature on the compressive strength of a certain type of concrete. Five concrete specimens are cured at each of four temperatures, and the compressive
An experiment was performed to determine whether the annealing temperature of ductile iron affects its tensile strength. Five specimens were annealed at each of four temperatures. The tensile
Refer to Exercise 13. a. Compute the quantity s =√MSE, the estimate of the error standard deviation σ. b. Assuming s to be the error standard deviation, find the sample size necessary in each
The article "Multi-objective Scheduling Problems: Determination of Pruned Pareto Sets" (H. Taboada and D. Coit, IIE Transactions, 2008:552-564), presents examples in a discussion of optimization
The article "Solid-Phase Chemical Fractionation of Selected Trace Metals in Some Northern Kentucky Soils" (A. Karathanasis and J. Pils, Soil and Sediment Contamination, 2005:293-308) presents pH
The removal of ammoniacal nitrogen is an important aspect of treatment of leachate at landfill sites. The rate of removal (in percent per day) is recorded for several days for each of several
The article "Influence of Age on Masonry Bond Strength and Mortar Microstructure" (H. Sugo, A. Page, and S. Lawrence, Can J Civ Eng, 2007:1433-1442) investigates the effect of age on tensile strength
The article "Secretion of Parathyroid Hormone Oscillates Depending on the Change in Serum Ionized Calcium During Hemodialysis and May Affect Bone Metabolism" (T. Kitahara, K, Ueki et al., Nephron
A certain chemical reaction was run three times at each of three temperatures. The yields, expressed as a percent of a theoretical maximum, were as follows:a. Construct an ANOVA table. You may give a
The article "Organic Recycling for Soil Quality Conservation in a Sub-Tropical Plateau Region" (K. Chakrabarti, B. Sarkar, et al., J. Agronomy and Crop Science, 2000:137-142) reports an experiment in
Refer to Exercise 16 in Section 9.1. a. Use the Fisher LSD method to find a 95% confidence interval for the difference between the means for a diameter of 16 and a diameter of 36. b. Use the
In an experiment to determine the effect of catalyst on the yield of a certain reaction, the mean yields for reactions run with each of four catalysts were X̅1. = 89.88, X̅2. = 89.51, X̅3. =
For some data sets, the F statistic will reject the null hypothesis of no difference in mean yields, but the Tukey-Kramer method will not find any pair of means that can be concluded to differ. For
Acrylic resins used in the fabrication of dentures should not absorb much water, since water sorption reduces strength. The article "Reinforcement of Acrylic Resin for Provisional Fixed Restorations.
Refer to Exercise 13 in Section 9.1. a. Use the Bonferroni method to determine which pairs of means, if any, are different at the 5% level. b. Use the Tukey-Kramer method to determine which pairs of
Refer to Exercise 13 in Section 9.1.Ametallurgistwants to determine whether the mean tensile strength for specimens annealed at 900◦C differs from the mean strengths for specimens annealed at
Refer to Exercise 5 in Section 9.1. a. Use the Fisher LSD method to find a 95% confidence interval for the difference between the means for specimens aged 3 days and specimens aged 365 days. b. Use
To assess the effect of piston ring type and oil type on piston ring wear, three types of piston ring and four types of oil were studied. Three replications of an experiment, in which the number of
Artificial joints consist of a ceramic ball mounted on a taper. The article "Friction in Orthopaedic Zirconia Taper Assemblies" (W. Macdonald, A. Aspenberg, et al., Proceedings of the Institution of
Refer to Exercise 12. The treatments with a delivery ratio of 1:0 were controls, or blanks. It was discovered after the experiment that the high apparent levels of sorption in these controls was

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