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modern mathematical statistics with applications

Questions and Answers of Modern Mathematical Statistics With Applications

In an article in IEEE Transactions on Instrumentation and Measurement (2001, Vol. 50, pp. 2033–2040) powdered mixtures of coal and limestone were analyzed for permittivity.The errors in the density
Data from a patient satisfaction survey in a hospital are shown in the following table:The regressor variables are the patient’s age, an illness severity index (larger values indicate greater
The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year’s usage and temperature are shown
Obtain time-ordered data from a process of interest. Use the data to construct appropriate control charts and comment on the control of the process. Can you make any recommendations to improve the
Consider the following Minitab ANOVA table used to analyze multiple measurements on each of 10 parts.(a) How many replicate measurements were made of these 10 parts?(b) Estimate (c) What percentage
An implantable defibrillator is a small unit that senses erratic heart signals from a patient. If the signal does not normalize within a few seconds, the unit charges itself to 650 V and delivers a
Consider an control chart with UCL 17.98, LCL 12.31, and n 4. Suppose that the mean shifts to 12.8.X r 3.895, X r 0.39, X ˆ 2.922, X X (a) What is the probability that this shift will be
Samples of size n 6 are collected from a process every hour. After 20 samples have been collected, we calculate. Find trial control limits for and R charts.
Consider the experiment in Exercise 7-2. Suppose that the experiment was actually carried out on three types of drying times and two types of paint. The data are the following:(a) Perform the
In their book, Empirical Model Building and Response Surfaces (Hoboken, NJ: John Wiley & Sons, 1987), G. E. P. Box and N. R. Draper describe an experiment with three factors. The data shown in
An article in Tappi (Vol. 43, 1960, pp. 38–44)describes an experiment that investigated the ash value of paper pulp (a measure of inorganic impurities). Two variables, temperature T in degrees
A manufacturer of cutting tools has developed two empirical equations for tool life (y1) and tool cost (y2). Both models are functions of tool hardness (x1) and manufacturing time (x2). The equations
Consider the experimental design in the table that follows. This experiment was run in a chemical process.(a) The response y1 is the viscosity of the product. Fit an appropriate response surface
An article in Rubber Age (Vol. 89, 1961, pp. 453–458)describes an experiment on the manufacture of a product in which two factors were varied: reaction time (hr) and temperature(C). These factors
An article in the Journal of Marketing Research(1973, Vol. 10, No. 3, pp. 270–276) presented a 274 fractional factorial design to conduct marketing research:The factor and levels are shown in the
Suppose that in Exercise 7-14 it was possible to run only a fraction of replicate I for the 24 design. Construct the design and use only the data from the eight runs you have generated to perform the
Montgomery (2009a) describes a 241 fractional factorial design used to study four factors in a chemical process.The factors are A temperature, B pressure, C concentration, and D stirring rate,
R. D. Snee (“Experimenting with a Large Number of Variables,” in Experiments in Industry: Design, Analysis and Interpretation of Results, by R. D. Snee, L. D. Hare, and J. B.Trout, eds., ASQC,
An article in Advanced Semiconductor Manufacturing Conference (ASMC) (May 2004, pp. 325–29) stated that dispatching rules and rework strategies are two major operational elements that impact
Consider the following Minitab output from a single replicate of a 24 experiment in two blocks with ABCD confounded.(a) Comment on the value of blocking in this experiment.(b) What effects were used
Consider the Minitab analysis results of a -designed experiment with two replicates at the corner points and four replicates at a center point.(a) Find all of the missing values for the t-tests and
Consider the data from Exercise 7-13, replicate I only.Suppose that a center point (with four replicates) is added to these eight runs. The tool life response at the center point is 425, 400, 437,
Consider the semiconductor experiment in Exercise 7-18. Suppose that a center point (replicated five times) could be added to this design and that the responses at the center are 45, 40, 41, 47, and
An article in Talanta (2005, Vol. 65, pp. 895–899)presented a 23 factorial design to find lead level by using flame atomic absorption spectrometry (FAAS). The data are shown in the following
An experiment was run in a semiconductor fabrication plant in an effort to increase yield. Five factors, each at two levels, were studied. The factors (and levels) were A aperture setting (small,
Consider a famous experiment reported by O. L. Davies(ed.), The Design and Analysis of Industrial Experiments(London: Oliver and Boyd, 1956). The following data were collected from an unreplicated
The data shown here represent a single replicate of a 25 design that is used in an experiment to study the compressive strength of concrete. The factors are mix (A), time (B), laboratory (C),
Four factors are thought to influence the taste of a soft-drink beverage: type of sweetener (A), ratio of syrup to water (B), carbonation level (C), and temperature (D). Each factor can be run at two
An engineer is interested in the effect of cutting speed(A), metal hardness (B), and cutting angle (C) on the life of a cutting tool. Two levels of each factor are chosen, and two replicates of a 23
Consider the ANOVA in Exercise 7-10. (a) Calculate the sum of squares, mean squares, and F-statistic for the A, B, and AB effects. (b) How does the sum of squares of regression relate to the sum of
Consider the ANOVA table in Exercise 7-9. (a)Calculate the sum of squares, mean squares, and F-test for main effects (the pooled A and B effects). (b) Assume that the current residual error is
Consider the analysis of a designed experiment with 5 replicates. Use the following partially complete Minitab output to answer the following questions.(a) Find all of the missing values in the
Consider the analysis of a designed experiment with 3 replicates. Use the following partially complete Minitab output to answer the following questions.(a) Find all of the missing values in the
An article in the IEEE Transactions on Semiconductor Manufacturing (Vol. 5, No. 3, 1992, pp. 214–222) describes an experiment to investigate the surface charge on a silicon wafer.The factors
A article in the IEEE Transactions on Electron Devices(Vol. ED-33, 1986, p. 1754) describes a study on the effects of two variables—polysilicon doping and anneal conditions(time and
An article in the Journal of Testing and Evaluation(Vol. 16, No. 6, 1988, pp. 508–515) investigated the effects of cyclic loading frequency and environmental conditions on fatigue crack growth at a
Johnson and Leone (Statistics and Experimental Design in Engineering and the Physical Sciences, John Wiley, 1977) describe an experiment conducted to investigate warping of copper plates. The two
An experiment was conducted to determine whether either firing temperature or furnace position affects the baked density of a carbon anode. The data are as follows:(a) Compute the estimates of the
An experiment was designed to identify a better ultrafiltration membrane for separating proteins and peptide drugs from fermentation broth. Two levels of an additive PVP (% wt)and time duration
An engineer suspects that the surface finish of metal parts is influenced by the type of paint used and the drying time. She selects two drying times—20 and 30 minutes—and uses two types of
An experiment involves a storage battery used in the launching mechanism of a shoulder-fired ground-to-air missile.Two material types can be used to make the battery plates. The objective is to
Identify a situation in which two or more variables of interest may be related but the mechanistic model relating the variables is unknown. Collect a random sample of data for these variables and
An article in Cancer Epidemiology, Biomarkers and Prevention (Vol. 5, 1996, pp. 849–852) describes a pilot study to assess the use of toenail arsenic concentrations as an indicator of ingestion of
An article in Electronic Packaging and Production(Vol. 42, 2002) reported the effect of X-ray inspection of integrated circuits. The rads (radiation dose) were studied as a function of current (in
Consider the simple linear regression model Y0 1x . Suppose that the analyst wants to use as the regressor variable.(a) Using the data in Exercise 6-51, construct one scatter plot of the (xi,
A rocket motor is manufactured by bonding together two types of propellants, an igniter and a sustainer. The shear strength of the bond y is thought to be a linear function of the age of the
Consider the no-intercept model Yxwith the ’s NID(0, 2). The estimate of 2 is s2 and(a) Devise a test statistic for H0: 0 versus H1: 0.(b) Apply the test in part (a) to the model from
An article in the Journal of Environmental Engineering(Vol. 115, No. 3, 1989, pp. 608–619) reported the results of a study on the occurrence of sodium and chloride in surface streams in central
Following are data on y green liquor (g/l) and x paper machine speed (ft/min) from a Kraft paper machine.(The data were read from a graph in an article in the Tappi Journal, March 1986.)(a) Fit the
Consider the engine thrust data in Exercise 6-46. Refit the model using y* ln y as the response variable and x*3 ln x3 as the regressor (along with x4 and x5).(a) Test for significance of
The data shown in Table 6-15 represent the thrust of a jet-turbine engine (y) and six candidate regressors: x1 primary speed of rotation, x2 secondary speed of rotation, x3 fuel flow rate, x4
The hii are often used to denote leverage—that is, a point that is unusual in its location in the x-space and that may be influential. Generally, the ith point is called a leverage point if hii
The data that follow are DC output from a windmill (y)and wind velocity (x).(a) Draw a scatter diagram of these data. What type of relationship seems appropriate in relating y to x?(b) Fit a simple
Studentized Residuals. Show that in a simple linear regression model the variance of the ith residual is(a) Explain why ri has unit standard deviation (for known).(b) Do the standardized residuals
Suppose that the simple linear regression model has been fit to n 25 observations and R2 0.90.(a) Test for significance of regression at 0.05. Use the results of Exercise 6-41.(b) What is the
An industrial engineer at a furniture manufacturing plant wishes to investigate how the plant’s electricity usage depends on the amount of the plant’s production. He suspects that there is a
A mechanical engineer is investigating the surface finish of metal parts produced on a lathe and its relationship to the speed (in revolutions per minute) and type of cutting tool of the lathe. The
Consider the HFE data in Exercise 6-22.
Consider the power consumption data in Exercise 6-21.
Consider the density data in Exercise 6-20.
Consider the patient satisfaction survey data in Exercise 6-19.
Consider the MPG data and multiple linear regression problem in Exercises 6-18 and 6-24.For Exercises 6-35 to 6-38, using only first-order terms, build regression models using the following
Consider the bearing wear data and multiple linear regression problem in Exercises 6-17 and 6-23.(a) Fit second-order polynomial models.(b) Check for multicolliearity in the data for each of the
Use the following partially complete Minitab output to answer the following questions.(a) Find all of the missing values.(b) Find the estimate of(c) Test for significance of regression. Use(d) Test
Use the following partially complete Minitab output to answer the following questions.(a) Find all of the missing values.(b) Find the estimate of(c) Test for significance of regression. Use 0.05.
An article in Biotechnology Progress (Vol. 17, 2001, pp. 366–368) reported an experiment to investigate and optimize nisin extraction in aqueous two-phase systems (ATPS).The nisin recovery was the
An article in Optical Engineering (“Operating Curve Extraction of a Correlator’s Filter,” Vol. 43, 2004, pp.2775–2779) reported the use of an optical correlator to perform an experiment by
Consider the HFE data and multiple linear regression model in Exercise 6-22.(a) Find the mean HFE given that x1 14.5, x2 220, and x3 5.0.(b) Compute a 90% CI on this mean response.(c) Compute a
Consider the power consumption data and multiple linear regression model in Exercise 6-21.(a) Find the mean power consumption given that x1 75F, x2 24 days, x3 90%, and x4 98 tons.(b)
Consider the density data in Exercise 6-20.(a) Estimate the mean density given that dielectric constant 2.4 and loss factor 0.025.(b) Compute a 95% CI on this mean response.(c) Compute a 95% PI on
Consider the patient satisfaction survey data in Exercise 6-19(a) Estimate the mean satisfaction given that age 24, severity 38, Surg-Med 0, and anxiety 2.8.(b) Compute a 95% CI on this mean
Consider the MPG data and multiple linear regression model in Exercise 6-18.(a) Find the mean MPG given that the weight is 2650 and the horsepower is 120.(b) Compute a 95% CI on this mean
Consider the bearing wear data and multiple linear regression model in Exercise 6-17.(a) Find the mean bearing wear given that the oil viscosity is 25.0 and the load is 1100.(b) Compute a 99% CI on
An engineer at a semiconductor company wants to model the relationship between the device HFE (y) and three parameters: Emitter-RS (x1), Base-RS (x2), and Emitter-to-Base RS (x3). The data are shown
The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature(x1), the number of days in the month (x2), the average product purity (x3), and
Consider the MPG data in Exercise 2-54.(a) Estimate the regression coefficients. Write the multiple linear regression model. Comment on the relationship found between the set of independent variables
Consider the bearing wear data in Exercise 2-53. (a) Estimate the regression coefficients. Write the multiple linear regression model. Comment on the relationship found between the set of independent
Use the following partially complete Minitab output to answer the following questions.(a) Find all of the missing values.(b) Find the estimate of(c) Test for significance of regression. Test for
Use the following partially complete Minitab output to answer the following questions.(a) Find all of the missing values.(b) Find the estimate of(c) Test for significance of regression. Test for
An article in the Journal of the Environmental Engineering Division (“Least Squares Estimates of BOD Parameters,” Vol. 106, 1980, pp. 1197–1202) describes the results of testing a sample from
An article in Wood Science and Technology (“Creep in Chipboard, Part 3: Initial Assessment of the Influence of Moisture Content and Level of Stressing on Rate of Creep and Time to Failure,” Vol.
Consider the data and simple linear regression model in Exercise 6-6.(a) Find the mean rise in blood pressure given that the sound pressure level is 85 decibels.(b) Compute a 99% CI on this mean
Consider the data and simple linear regression model in Exercise 6-5.(a) Find the mean permeability given that the strength is 2.1.(b) Compute a 99% CI on this mean response.(c) Compute a 99% PI on a
Consider the data and simple linear regression in Exercise 6-4.(a) Find the mean turbidity given that the temperature is 25.0 degrees.(b) Compute a 95% CI on this mean response.(c) Compute a 95% PI
Consider the data and simple linear regression in Exercise 6-3.(a) Find the mean deflection given that the temperature is 74.0 degrees.(b) Compute a 95% CI on this mean response.(c) Compute a 95% PI
Consider the data and simple linear regression model in Exercise 6-2.(a) Find the mean pounds of steam given that the ambient temperature is 52 degrees.(b) Compute a 99% CI on this mean response.(c)
Consider the data and simple linear regression in Exercise 6-1.(a) Find the mean thermal conductivity given that the product density is 0.2350.(b) Compute a 95% CI on this mean response.(c) Compute a
An article in the Journal of Sound and Vibration (Vol. 151, 1991, pp. 383–394) described a study investigating the relationship between noise exposure and hypertension. The following data are
An article in Concrete Research (“Near Surface Characteristics of Concrete: Intrinsic Permeability,” Vol. 41, 1989) presented data on compressive strength x and intrinsic permeability y of
Turbidity is a measure of the cloudiness of the water and is used to indicate water quality levels. Higher turbidity levels are usually associated with higher levels of disease- causing microbes like
Regression methods were used to analyze the data from a study investigating the relationship between roadway surface temperature (x) and pavement deflection ( y). The data follow.(a) Estimate the
Establishing the properties of materials is an important problem in identifying a suitable substitute for biodegradable materials in the fast-food packaging industry. Consider the following data on
Identify an example in which a comparative standard or claim is made about two independent populations.For example, Car Type A gets more average miles per gallon in urban driving than Car Type B. The
An article appeared in The Wall Street Journal on Tuesday, April 27, 2010, with the title “Eating Chocolate Is Linked to Depression.” The article reported on a study funded by the National Heart,
The two-sample z-test in Section 5-2 can be viewed as a large sample test for the difference in means.Suppose that we need to compare the means of two independent Poisson distributions. Let be a
Consider the graph of the global mean surface air temperature anomaly shown in Figure 2-1. Suppose that the data were separated into two segments: 1880–1940 and 1941–2004. You are asked to use
Reconsider the data in Exercise 5-89. Suppose that any resistor below 100 ohms is considered defective.(a) Estimate the fraction of defective resistors produced by each vendor.(b) Construct a 95%
A team of computer engineers is interested in determining if the percentage of disk space that is used for virtual memory will significantly improve the response time of a server. The team measured
An article in Environment International (Vol. 18, No. 4, 1992) describes an experiment in which the amount of radon released in showers was investigated. Radon-enriched water was used in the
A paper in the Journal of the Association of Asphalt Paving Technologists (Vol. 59, 1990) describes an experiment to determine the effect of air voids on percentage retained strength of asphalt. For

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