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# Solutions for Chapter 14-4: TWO-FACTOR FACTORIAL EXPERIMENTS

## Full solutions for Applied Statistics and Probability for Engineers | 3rd Edition

ISBN: 9780471204541

Solutions for Chapter 14-4: TWO-FACTOR FACTORIAL EXPERIMENTS

Solutions for Chapter 14-4
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##### ISBN: 9780471204541

This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 3. Since 10 problems in chapter 14-4: TWO-FACTOR FACTORIAL EXPERIMENTS have been answered, more than 22147 students have viewed full step-by-step solutions from this chapter. Chapter 14-4: TWO-FACTOR FACTORIAL EXPERIMENTS includes 10 full step-by-step solutions. 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: 9780471204541.

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

A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

• All possible (subsets) regressions

A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

• Alternative hypothesis

In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

• Attribute control chart

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

• 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

• Bernoulli trials

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

• Bias

An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

• Chance cause

The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

• 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

• Completely randomized design (or experiment)

A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

• Conditional variance.

The variance of the conditional probability distribution of a random variable.

• Consistent estimator

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

• 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.

• Defect concentration diagram

A quality tool that graphically shows the location of defects on a part or in a process.

• Dependent variable

The response variable in regression or a designed experiment.

• 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 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.

• 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.

• 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.

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