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introduction to probability statistics

Questions and Answers of Introduction To Probability Statistics

Coir fiber, derived from coconut, is an eco-friendly material with great potential for use in construction. The article“Seepage Velocity and Piping Resistance of Coir Fiber Mixed Soils” (J. of
The article “Sensitivity Analysis of a 2.5 kW Proton Exchange Membrane Fuel Cell Stack by Statistical Method” (J. of Fuel Cell Sci. and Tech., 2009: 1–6) used regression analysis to investigate
The article “Chemithermomechanical Pulp from Mixed High Density Hardwoods” (TAPPI, July 1988: 145–146)reports on a study in which the accompanying data was obtained to relate to NaOH used as a
The effect of manganese (Mn) on wheat growth is examined in the article “Manganese Deficiency and Toxicity Effects on Growth, Development and Nutrient Composition in Wheat” (Agronomy J., 1984:
Conductivity is one important characteristic of glass. The article “Structure and Properties of Rapidly Quenched Li2O-Al2ONb2O5 Glasses” (J. of the Amer. Ceramic Soc., 1983: 890–892)202.88 sYˆ
The accompanying data on and power (W) for a certain laser configuration was read from a graph in the article “Frequency Dependence in RF Discharge Excited Waveguide CO2 Lasers” (IEEE J. of
The article “An Experimental Study of Resistance Spot Welding in 1 mm Thick Sheet of Low Carbon Steel” (J. of Engr. Manufacture, 1996: 341–348) discussed a statistical analysis whose basic aim
An ammonia bath is the one most widely used for depositing Pd-Ni alloy coatings. The article “Modelling of Palladium and Nickel in an Ammonia Bath in a Rotary Device” (Plating and Surface
An aeronautical engineering student carried out an experiment to study how ratio related to the variables of a certain forward lifting surface relative to the main wing and placement relative to the
Feature recognition from surface models of complicated parts is becoming increasingly important in the development of efficient computer-aided design (CAD) systems.The article “A Computationally
The article “Validation of the Rockport Fitness Walking Test in College Males and Females” (Research Quarterly for Exercise and Sport, 1994: 152–158) recommended the following estimated
The authors of the article “Long-Term Effects of Cathodic Protection on Prestressed Concrete Structures” (Corrosion, 1997: 891–908) presented a scatter plot of permeation flux (mA/cm2) versus
Refer to the water-discharge data given in Exercise 55 and let , and . Consider fitting the model .a. The resulting hii’s are .138, .302, .266, .604, .464, .360,.215, .153, .214, and .284. Does any
A study carried out to investigate the relationship between a response variable relating to pressure drops in a screen-plate bubble column and the predictors fluid velocity, viscosity, and mesh size
For each method, explain what occurred at every iteration of the algorithm
The accompanying Minitab output resulted from applying both the backward elimination method and the forward selection method to the wood specific gravity data referred to in Exercise
Minitab’s Best Regression option was used on the wood specific gravity data referred to in Exercise 56, resulting in the accompanying output. Which model(s) would you recommend for investigating in
The article “Response Surface Methodology for Protein Extraction Optimization of Red Pepper Seed” (Food Sci. and Tech., 2010: 226–231) gave data on the response variable and the independent
In the accompanying table, we give the smallest SSE for each number of predictors for a regression problem in which heat of hardening in cement, tricalcium aluminate, tricalcium silicate, aluminum
In an experiment to study factors influencing wood specific gravity (“Anatomical Factors Influencing Wood Specific Gravity of Slash Pines and the Implications for the Development of a High-Quality
The article “Bank Full Discharge of Rivers” (Water Resources J., 1978: 1141–1154) reports data on discharge amount (q, in m3/sec), flow area (a, in m2), and slope of the water surface (b, in
The use of high-strength steels (HSS) rather than aluminum and magnesium alloys in automotive body structures reduces vehicle weight. However, HSS use is still problematic because of difficulties
Snowpacks contain a wide spectrum of pollutants that may represent environmental hazards. The article “Atmospheric PAH Deposition: Deposition Velocities and Washout Ratios” (J. of Environmental
Utilization of sucrose as a carbon source for the production of chemicals is uneconomical. Beet molasses is a readily available and low-priced substitute. The article “Optimization of the
The article “The Undrained Strength of Some Thawed Permafrost Soils” (Canadian Geotechnical J., 1979:420–427) contains the following data on undrained shear strength of sandy soil (y, in kPa),
a. When the model is fit to the hops data of Exercise 49, the estimate of b5 is with estimated standard deviation . Test versus.b. Each t ratio for the model of part(a) is less than 2 in absolute
The article “The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hops (Agric. Meteor. 1974:375–382) reports the following data on yield (y), mean temperature over the period
An experiment to investigate the effects of a new technique for degumming of silk yarn was described in the article “Some Studies in Degumming of Silk with Organic Acids” (J. Society of Dyers and
Efficient design of certain types of municipal waste incinerators requires that information about energy content of the waste be available. The authors of the article “Modeling the Energy Content
A regression analysis carried out to relate for a water filtration system (hr) to since the previous service (months) and of repair (1 if electrical and 0 if mechanical) yielded the following model
The accompanying Minitab regression output is based on data that appeared in the article “Application of Design of Experiments for Modeling Surface Roughness in Ultrasonic Vibration Turning” (J.
An experiment carried out to study the effect of the mole contents of cobalt (x1) and the calcination temperature (x2)on the surface area of an iron-cobalt hydroxide catalyst (y)resulted in the
An investigation of a die-casting process resulted in the accompanying data on ,, and difference on the die surface (“A Multiple-Objective Decision-Making Approach for Assessing Simultaneous
The ability of ecologists to identify regions of greatest species richness could have an impact on the preservation of genetic diversity, a major objective of the World Conservation Strategy. The
The article “Readability of Liquid Crystal Displays: A Response Surface” (Human Factors, 1983: 185–190) used a multiple regression model with four independent variables to study accuracy in
Let at a fast-food outlet (1000s of $), of competing outlets within a 1-mile radius, within a 1-mile radius (1000s of people), and x3 be an indicator variable that equals 1 if the outlet has a
Let life of a bearing, , and. Suppose that the multiple regression model relating life to viscosity and load isa. What is the mean value of life when viscosity is 40 and load is 1100?b. When
A trucking company considered a multiple regression model for relating the dependent variable daily travel time for one of its drivers (hours) to the predictors traveled (miles) and of deliveries
Cardiorespiratory fitness is widely recognized as a major component of overall physical well-being. Direct measurement of maximal oxygen uptake (VO2max) is the single best measure of such fitness,
The article “The Respiration in Air and in Water of the Limpets Patella caerulea and Patella lusitanica” (Comp.Biochemistry and Physiology, 1975: 407–411) proposed a simple power model for the
The following data resulted from an experiment to assess the potential of unburnt colliery spoil as a medium for plant growth. The variables are extractable cations and acidity/total cation exchange
In many polynomial regression problems, rather than fitting a “centered” regression function using , computational accuracy can be improved by using a function of the standardized independent
The following data is a subset of data obtained in an experiment to study the relationship between x 5 soil pH and. Concentration/EC (“Root Responses of Three Gramineae Species to Soil Acidity in
The accompanying data on output (W) and difference (°K) was provided by the authors of the article “Comparison of Energy and Exergy Efficiency for Solar Box and Parabolic Cookers” (J. of Energy
The accompanying data was extracted from the article“Effects of Cold and Warm Temperatures on Springback of Aluminum-Magnesium Alloy 5083-H111” (J. of Engr.Manuf., 2009: 427–431). The response
High-alumina refractory castables have been extensively investigated in recent years because of their significant advantages over other refractory brick of the same class—lower production and
The viscosity (y) of an oil was measured by a cone and plate viscometer at six different cone speeds (x). It was assumed that a quadratic regression model was appropriate, and the estimated
The following data on concentration (g/L) and time (days) for a particular blend of malt liquor was read from a scatter plot in the article “Improving Fermentation Productivity with Reverse
The article “Physical Properties of Cumin Seed” (J. of Agric.Engr. Res., 1996: 93–98) considered a quadratic regression of density on y 5 bulk x 5 moisture content. Data from a graph in the
The article “Acceptable Noise Levels for Construction Site Offices” (Building Serv. Engr. Res. Tech., 2009:87–94) analyzed responses from a sample of 77 individuals, each of whom was asked to
Kyphosis refers to severe forward flexion of the spine following corrective spinal surgery. A study carried out to determine risk factors for kyphosis reported the accompanying ages (months) for 40
Suppose x and y are related according to a probabilistic exponential model , with a constant independent of x (as was the case in the simple linear model. Is V(Y) a constant independent of x [as was
In each of the following cases, decide whether the given function is intrinsically linear. If so, identify x and y, and then explain how a random error term can be introduced to yield an
A plot in the article “Thermal Conductivity of Polyethylene:The Effects of Crystal Size, Density, and Orientation on the Thermal Conductivity” (Polymer Engr. and Science, 1972:204–208) suggests
Polyester fiber ropes are increasingly being used as components of mooring lines for offshore structures in deep water.The authors of the paper “Quantifying the Residual Creep Life of Polyester
Failures in aircraft gas turbine engines due to high cycle fatigue is a pervasive problem. The article “Effect of Crystal Orientation on Fatigue Failure of Single Crystal Nickel Base Turbine Blade
No tortilla chip aficionado likes soggy chips, so it is important to find characteristics of the production process that produce chips with an appealing texture. The following data on time (sec) and
If there is at least one x value at which more than one observation has been made, there is a formal test procedure for testing for some values , (the true regression function is linear)versus Ha: H0
Consider the following four (x, y) data sets; the first three have the same x values, so these values are listed only once(Frank Anscombe, “Graphs in Statistical Analysis,”Amer.Statistician,
Recall that has a normal distribution with expected value and variance so that Z 5 bˆ0 1 bˆ1x 2 (b0 1 b1x)s° 1 n1 (x 2 x) 2 g(xi 2 x) 2 ¢1/2 s2 • 1 n1 (x 2 x) 2 g(xi 2 x) 2¶b0 1 b1x bˆ0 1
a. Express the ith residual (where )in the form , a linear function of the Yj’s. Then use rules of variance to verify that is given by Expression (13.2).b. It can be shown that and (the ith
a. Show that when the ei’s are the residuals from a simple linear regression.b. Are the residuals from a simple linear regression independent of one another, positively correlated, or negatively
Continuous recording of heart rate can be used to obtain information about the level of exercise intensity or physical strain during sports participation, work, or other daily activities. The
The accompanying scatter plot is based on data provided by authors of the article “Spurious Correlation in the USEPA Rating Curve Method for Estimating Pollutant Loads” (J. of Envir. Engr., 2008:
As the air temperature drops, river water becomes supercooled and ice crystals form. Such ice can significantly affect the hydraulics of a river. The article “Laboratory Study of Anchor Ice
Wear resistance of certain nuclear reactor components made of Zircaloy-2 is partly determined by properties of the oxide layer. The following data appears in an article that proposed a new
Example 12.6 presented the residuals from a simple linear regression of moisture content y on filtration rate x.a. Plot the residuals against x. Does the resulting plot suggest that a straight-line
Suppose the variables and time are related according to the simple linear regression model with .a. If observations are made at the x values x1 5 5, x2 5 10, x2 5 15, x2 5 20, and , calculate the
Reconsider the situation of Exercise 73, in which x retained austenite content using a garnet abrasive and y abrasive wear loss were related via the simple linear regression model . Suppose that for
In biofiltration of wastewater, air discharged from a treatment facility is passed through a damp porous membrane that causes contaminants to dissolve in water and be transformed into harmless
Use the formula for computing SSE to verify that.
Verify that the t statistic for testing in Section 12.3 is identical to the t statistic in Section 12.5 for testing.
Let sx and sy denote the sample standard deviations of the observed x’s and y’s, respectively [that is, and similarly for ].a. Show that an alternative expression for the estimated regression
Show that , which gives an alternative computational formula for SSE.
In Section 12.4, we presented a formula for and a CI for . Taking gives and a CI for b0. Use the data of Example 12.11 to calculate the estimated standard deviation of and a 95% CI for the
The article “Photocharge Effects in Dye Sensitized Ag[Br,I]Emulsions at Millisecond Range Exposures” (Photographic Sci. and Engr., 1981: 138–144) gives the accompanying data on light absorption
An investigation was carried out to study the relationship between speed (ft/sec) and stride rate (number of steps taken/sec) among female marathon runners. Resulting summary quantities included, and
The accompanying data was read from a scatter plot in the article “Urban Emissions Measured with Aircraft” (J. of the Air and Waste Mgmt. Assoc., 1998: 16–25). The response variable is , and
The SAS output at the bottom of this page is based on data from the article “Evidence for and the Rate of Denitrification in the Arabian Sea” (Deep Sea Research, 1978: 431–435). The variables
The accompanying data on x diesel oil consumption rate measured by the drain–weigh method and y rate measured by the CI-trace method, both in g/hr, was read from a graph in the article “A New
Forensic scientists are often interested in making a measurement of some sort on a body (alive or dead) and then using that as a basis for inferring something about the age of the body. Consider the
The appraisal of a warehouse can appear straightforward compared to other appraisal assignments. A warehouse appraisal involves comparing a building that is primarily an open shell to other such
A sample of pairs was collected and a test of versus was carried out. The resulting P-value was computed to be .00032.a. What conclusion would be appropriate at level of significance .001?b. Does
Consider a time series—that is, a sequence of observations obtained over time—with observed values . Suppose that the series shows no upward or downward trend over time. An investigator will
Torsion during hip external rotation and extension may explain why acetabular labral tears occur in professional athletes. The article “Hip Rotational Velocities During the Full Golf Swing” (J.
The article “Increases in Steroid Binding Globulins Induced by Tamoxifen in Patients with Carcinoma of the Breast” (J.of Endocrinology, 1978: 219–226) reports data on the effects of the drug
Hydrogen content is conjectured to be an important factor in porosity of aluminum alloy castings. The article “The SReduced Pressure Test as a Measuring Tool in the Evaluation of Porosity/Hydrogen
The authors of the paper “Objective Effects of a Six Months’ Endurance and Strength Training Program in Outpatients with Congestive Heart Failure” (Medicine and Science in Sports and Exercise,
Head movement evaluations are important because individuals, especially those who are disabled, may be able to operate communications aids in this manner. The article “Constancy gyi 5 47.92, gyi 2
Toughness and fibrousness of asparagus are major determinants of quality. This was the focus of a study reported in“Post-Harvest Glyphosphate Application Reduces Toughening, Fiber Content, and
The article “Bone Density and Insertion Torque as Predictors of Anterior Cruciate Ligament Graft Fixation Strength” (The Amer. J. of Sports Med., 2004: 1421–1429)gave the accompanying data on
Verify that is indeed given by the expression in the text. [Hint: .]
The decline of water supplies in certain areas of the United States has created the need for increased understanding of relationships between economic factors such as crop yield and hydrologic and
Plasma etching is essential to the fine-line pattern transfer in current semiconductor processes. The article “Ion BeamAssisted Etching of Aluminum with Chlorine” (J. of the Electrochem. Soc.,
Refer to Example 12.12 in which x test track speed and y rolling test speed.a. Minitab gave and . Why is the former estimated standard deviation smaller than the latter one?sbˆ01bˆ1 s (47) 5 .186
Silicon-germanium alloys have been used in certain types of solar cells. The paper “Silicon-Germanium Films Deposited by Low-Frequency Plasma-Enhanced Chemical Vapor Deposition” (J. of Material
The catch basin in a storm-sewer system is the interface between surface runoff and the sewer. The catch-basin insert is a device for retrofitting catch basins to improve pollutantremoval properties.
The simple linear regression model provides a very good fit to the data on rainfall and runoff volume given in Exercise 16 of Section 12.2. The equation of the least squares line is, and .a. Use the
Astringency is the quality in a wine that makes the wine drinker’s mouth feel slightly rough, dry, and puckery. The paper “Analysis of Tannins in Red Wine Using Multiple Methods: Correlation with
Reconsider the filtration rate–moisture content data introduced in Example 12.6 (see also Example 12.7).a. Compute a 90% CI for , true average moisture content when the filtration rate is 125.b.

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