×
×

# Solutions for Chapter 13.3: Applied Statistics and Probability for Engineers 6th Edition

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

ISBN: 9781118539712

Solutions for Chapter 13.3

Solutions for Chapter 13.3
4 5 0 399 Reviews
16
0
##### ISBN: 9781118539712

Chapter 13.3 includes 8 full step-by-step solutions. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. Since 8 problems in chapter 13.3 have been answered, more than 174025 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
• Alias

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Biased estimator

Unbiased estimator.

• 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.

• Confounding

When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

• Convolution

A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

• 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.

• Critical value(s)

The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

• Defects-per-unit control chart

See U chart

• Degrees of freedom.

The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

• Dispersion

The amount of variability exhibited by data

• Empirical model

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

• Erlang random variable

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

• Error mean square

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

• Error variance

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

• 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.

• Expected value

The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

• Exponential random variable

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

• Finite population correction factor

A term in the formula for the variance of a hypergeometric random variable.

• 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.

• Frequency distribution

An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

×