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# Solutions for Chapter 13: Design and Analysis of Single-Factor Experiments: The Analysis of Variance

## Full solutions for Applied Statistics and Probability for Engineers | 5th Edition

ISBN: 9780470053041

Solutions for Chapter 13: Design and Analysis of Single-Factor Experiments: The Analysis of Variance

Solutions for Chapter 13
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##### ISBN: 9780470053041

This expansive textbook survival guide covers the following chapters and their solutions. Since 63 problems in chapter 13: Design and Analysis of Single-Factor Experiments: The Analysis of Variance have been answered, more than 24471 students have viewed full step-by-step solutions from this chapter. Chapter 13: Design and Analysis of Single-Factor Experiments: The Analysis of Variance includes 63 full step-by-step solutions. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers, edition: 5. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9780470053041.

Key Statistics Terms and definitions covered in this textbook
• Acceptance region

In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Attribute control chart

Any control chart for a discrete random variable. See Variables control chart.

• Categorical data

Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

• Cause-and-effect diagram

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

• Conidence level

Another term for the conidence coeficient.

• Crossed factors

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

• Decision interval

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

• Designed experiment

An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

• Discrete distribution

A probability distribution for a discrete random variable

• Distribution free method(s)

Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

• Error mean square

The error sum of squares divided by its number of degrees of freedom.

• Estimate (or point estimate)

The numerical value of a point estimator.

• Extra sum of squares method

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

• F distribution.

The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.

• First-order model

A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model

• 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 .

• Geometric random variable

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

• 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.

• Hat matrix.

In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .

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