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Solutions for Chapter 5.5: Statistics for Engineers and Scientists 4th Edition Full solutions for Statistics for Engineers and Scientists | 4th Edition

ISBN: 9780073401331 Solutions for Chapter 5.5

Solutions for Chapter 5.5
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ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Since 11 problems in chapter 5.5 have been answered, more than 614126 students have viewed full step-by-step solutions from this chapter. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Chapter 5.5 includes 11 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
• 2 k factorial experiment.

A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

• Backward elimination

A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

• Bivariate distribution

The joint probability distribution of two random variables.

• 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.

• Chi-square (or chi-squared) random variable

A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

• Conditional probability distribution

The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

• Contrast

A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

• Control limits

See Control chart.

• Covariance

A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

• 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.

• 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.

• Discrete distribution

A probability distribution for a discrete random variable

• Discrete random variable

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

• Distribution function

Another name for a cumulative distribution function.

• Eficiency

A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

• Error of estimation

The difference between an estimated value and the true value.

• Estimator (or point estimator)

A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

• Experiment

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

• Fisher’s least signiicant difference (LSD) method

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

• Generator

Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.