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# Solutions for Chapter 5.6: Statistics for Engineers and Scientists 4th Edition

## Full solutions for Statistics for Engineers and Scientists | 4th Edition

ISBN: 9780073401331

Solutions for Chapter 5.6

Solutions for Chapter 5.6
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##### ISBN: 9780073401331

Since 15 problems in chapter 5.6 have been answered, more than 442769 students have viewed full step-by-step solutions from this chapter. Chapter 5.6 includes 15 full step-by-step solutions. 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. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331.

Key Statistics Terms and definitions covered in this textbook
• Additivity property of x 2

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

• 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

• Attribute

A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

• 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

• Bayes’ theorem

An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

• Bimodal distribution.

A distribution with two modes

• Causal variable

When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

• 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.

• Central tendency

The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

• Chi-square test

Any test of signiicance based on the chi-square distribution. The most common chi-square 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

• Coeficient of determination

See R 2 .

• Comparative experiment

An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

• Continuity correction.

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

• Curvilinear regression

An expression sometimes used for nonlinear regression models or polynomial regression models.

• Density function

Another name for a probability density function

• Empirical model

A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• Forward selection

A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

• Goodness of fit

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.