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# Solutions for Chapter 9.5: 2p Factorial Experiments ## Full solutions for Statistics for Engineers and Scientists | 4th Edition

ISBN: 9780073401331 Solutions for Chapter 9.5: 2p Factorial Experiments

Solutions for Chapter 9.5
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##### ISBN: 9780073401331

This expansive textbook survival guide covers the following chapters and their solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since 13 problems in chapter 9.5: 2p Factorial Experiments have been answered, more than 283806 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Chapter 9.5: 2p Factorial Experiments includes 13 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
• Alias

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Arithmetic mean

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

• Assignable cause

The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

• Bivariate normal distribution

The joint distribution of two normal random variables

• Center line

A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

• Coeficient of determination

See R 2 .

• Conditional probability density function

The probability density function of the conditional probability distribution of a continuous random variable.

• 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

• Conidence level

Another term for the conidence coeficient.

• Consistent estimator

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

• Continuity correction.

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

• Continuous distribution

A probability distribution for a continuous random variable.

• Contour plot

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• Correlation matrix

A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

• 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 off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

• Crossed factors

Another name for factors that are arranged in a factorial experiment.

• Discrete random variable

A random variable with a inite (or countably ininite) range.

• Experiment

A series of tests in which changes are made to the system under study

• False alarm

A signal from a control chart when no assignable causes are present

• Geometric random variable

A discrete random variable that is the number of Bernoulli trials until a success occurs.

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