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# Solutions for Chapter 13.4: Applied Statistics and Probability for Engineers 6th Edition

## Full solutions for Applied Statistics and Probability for Engineers | 6th Edition

ISBN: 9781118539712

Solutions for Chapter 13.4

Solutions for Chapter 13.4
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##### ISBN: 9781118539712

Chapter 13.4 includes 27 full step-by-step solutions. Since 27 problems in chapter 13.4 have been answered, more than 146709 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712.

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

• Analysis of variance (ANOVA)

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

• 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.

• Consistent estimator

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

• Contingency table.

A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

• 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.

• Cook’s distance

In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

• 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.

• 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.

• Enumerative study

A study in which a sample from a population is used to make inference to the population. See Analytic study

• Error variance

The variance of an error term or component in a model.

• False alarm

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

• Gaussian distribution

Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

• Harmonic mean

The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .

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