 11.11.1.1: Use Table IV to determine whether these probabilities are greater t...
 11.11.1.2: Find the missing values in the analysis of variance table shown in ...
 11.11.1.3: Find the missing values in the analysis of variance table shown in ...
 11.11.1.4: A balanced experimental design has a sample size of n =12 observati...
 11.11.1.5: An experiment to compare k =4 factor levels has n1 =12 and x1 =16.0...
 11.11.1.6: An experiment to compare k =3 factor levels has n1 =17 and x1 =32.3...
 11.11.1.7: A balanced experimental design has a sample size of n =14 observati...
 11.11.1.8: A balanced experimental design has a sample size of n =11 observati...
 11.11.1.9: A balanced experimental design has a sample size of n =6 observatio...
 11.11.1.10: If each observation xij in a onefactor layout is replaced by the v...
 11.11.1.11: Consider the data set given in DS 11.1.1. (a) Calculate the sample ...
 11.11.1.12: Complete parts (a)(i) of 11.1.11 for the data set in DS 11.1.2.
 11.11.1.13: A factory has three production lines producing glass sheets that ar...
 11.11.1.14: A retail company is interested in examining whether the time taken ...
 11.11.1.15: Infrared Radiation Readings The data set in DS 11.1.3 concerns the ...
 11.11.1.16: Keyboard Layout Designs DS 11.1.4 gives the times taken to perform ...
 11.11.1.17: Dispersion Polymerization A chemical engineer is interested in how ...
 11.11.1.18: Computer Assembly Methods A computer manufacturer has production li...
 11.11.1.19: Three catalysts were compared to investigate how they affect the st...
 11.11.1.20: The data set in DS 11.1.7 is a oneway layout to compare the qualit...
 11.11.1.21: In a oneway layout to compare ve treatments an experiment gave n1 ...
 11.11.1.22: Metal Alloy Comparisons An experiment was performed to compare four...
 11.11.1.23: Durations of Investigatory Surgical Procedures Thirty patients with...
 11.11.1.24: E. Coli Colonies in Riverwater Four samples of water were taken at ...
 11.11.1.25: In a oneway layout, seven observations are taken from treatment 1 ...
 11.11.1.26: If the pvalue in the ANOVA table for a oneway analysis is larger ...
 11.11.1.27: Consider a oneway analysis of variance. (I) A pvalue larger than ...
 11.11.1.28: An analysis of variance can be used to compare: A. Two treatments w...
 11.11.2.1: Find the missing values in the analysis of variance table shown in ...
 11.11.2.2: Find the missing values in the analysis of variance table shown in ...
 11.11.2.3: A randomized block design has k =4 factor levels and b =10 blocks. ...
 11.11.2.4: A randomized block design has k =5 factor levels and b =15 blocks. ...
 11.11.2.5: A randomized block design has k =3 factor levels and b =8 blocks. T...
 11.11.2.6: Suppose that in a randomized block design the observations in the r...
 11.11.2.7: Consider the data set given in DS 11.2.1. (a) Calculate the factor ...
 11.11.2.8: Complete parts (a)(k) of 11.2.7 for the data set in DS 11.2.2. If t...
 11.11.2.9: Calciner Comparisons DS 11.2.3 gives a data set of brightness measu...
 11.11.2.10: Radar Detection of Airborne Objects A randomized block design is us...
 11.11.2.11: Golf Club Comparisons A total of b =9 golfers are each asked to hit...
 11.11.2.12: Production Line Assembly Methods A manufacturing company wants to i...
 11.11.2.13: Realtor Commissions A Realtor ofce has ve agents, and the manager w...
 11.11.2.14: Cleanliness Scores for Detergent Comparisons A chemical company run...
 11.11.2.15: Consider the following ANOVA table for a randomized block design.So...
 11.11.2.16: A randomized block design has k =3 factor levels and b =4 blocks. T...
 11.11.2.17: Consider a randomized block design with b blocks to compare k treat...
 11.11.2.18: A randomized block design has four factor levels with sample averag...
 11.11.2.19: Groundwater Pollution Levels An experiment was conducted to measure...
 11.11.5.1: Biaxial Nanowire Tests An experimenter measured the Youngs modulus ...
 11.11.5.2: Car Gas Efciencies A courier service buys four new cars of the same...
 11.11.5.3: Temperature Effect on Cement Curing An experiment is conducted to a...
 11.11.5.4: Fertilizer Comparisons A comparison of k =5 fertilizers is made in ...
 11.11.5.5: Red Blood Cell Adherence to Endothelial Cells A hospital has k =4 c...
 11.11.5.6: Insertion Gains of Hearing Aids The insertion gain of a hearing aid...
 11.11.5.7: Air Resistance Drag for Road Vehicles The reduction of drag from ai...
 11.11.5.8: Leather Shrinkage Measurements When leather is used to produce furn...
 11.11.5.9: Are the following statements true or false? (a) A oneway layout wi...
 11.11.5.10: Metal Alloy Hardness Tests The data set in DS 11.5.9 is a oneway l...
 11.11.5.11: A randomized block design has four factor levels with sample averag...
 11.11.5.12: Aquatic Radon Levels An investigation was conducted of the radon le...
 11.11.5.13: A completely randomized design to compare k =4 factor levels has n1...
 11.11.5.14: Volatile Organic Carbon Emissions Volatile organic carbon emissions...
 11.11.5.15: If the pvalue in the ANOVA table for a oneway analysis is less th...
 11.11.5.16: Consider a oneway analysis of variance. A. A pvalue larger than 1...
Solutions for Chapter 11: The Analysis of Variance
Full solutions for Probability and Statistics for Engineers and Scientists  4th Edition
ISBN: 9781111827045
Solutions for Chapter 11: The Analysis of Variance
Get Full SolutionsThis textbook survival guide was created for the textbook: Probability and Statistics for Engineers and Scientists, edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9781111827045. Since 63 problems in chapter 11: The Analysis of Variance have been answered, more than 11778 students have viewed full stepbystep solutions from this chapter. Chapter 11: The Analysis of Variance includes 63 full stepbystep solutions.

Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Biased estimator
Unbiased estimator.

Chance cause
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

Chisquare test
Any test of signiicance based on the chisquare distribution. The most common chisquare tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

Combination.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

Conidence interval
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

Control chart
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the incontrol value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be incontrol, or free from assignable causes. Points beyond the control limits indicate an outofcontrol process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

Counting techniques
Formulas used to determine the number of elements in sample spaces and events.

Covariance matrix
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the offdiagonal elements are the covariances between Xi and Xj . Also called the variancecovariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Critical value(s)
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

Estimate (or point estimate)
The numerical value of a point estimator.

Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

Fraction defective
In statistical quality control, that portion of a number of units or the output of a process that is defective.

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

Generating function
A function that is used to determine properties of the probability distribution of a random variable. See Momentgenerating function

Geometric mean.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .