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Solutions for Chapter 4.11: Applied Statistics and Probability for Engineers 6th Edition

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

ISBN: 9781118539712

Solutions for Chapter 4.11

Solutions for Chapter 4.11
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ISBN: 9781118539712

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. Since 14 problems in chapter 4.11 have been answered, more than 174614 students have viewed full step-by-step solutions from this chapter. Chapter 4.11 includes 14 full step-by-step solutions. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6.

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

A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

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.

• Bivariate distribution

The joint probability distribution of two random variables.

• Categorical data

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

• 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

• Consistent estimator

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

• 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.

• Correction factor

A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

• Correlation coeficient

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

• 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.

• Curvilinear regression

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

• 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.

• Deining relation

A subset of effects in a fractional factorial design that deine the aliases in the design.

• Dispersion

The amount of variability exhibited by data

• 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.

• 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.

• Exhaustive

A property of a collection of events that indicates that their union equals the sample space.

• 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.

• Factorial experiment

A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

• Fixed factor (or fixed effect).

In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

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