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# Solutions for Chapter 12: Analysis of Variance

## Full solutions for Elementary Statistics | 12th Edition

ISBN: 9780321836960

Solutions for Chapter 12: Analysis of Variance

Solutions for Chapter 12
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##### ISBN: 9780321836960

This expansive textbook survival guide covers the following chapters and their solutions. Since 10 problems in chapter 12: Analysis of Variance have been answered, more than 212155 students have viewed full step-by-step solutions from this chapter. Chapter 12: Analysis of Variance includes 10 full step-by-step solutions. Elementary Statistics was written by and is associated to the ISBN: 9780321836960. This textbook survival guide was created for the textbook: Elementary Statistics, edition: 12.

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

• Additivity property of x 2

If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

• 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

• Axioms of probability

A set of rules that probabilities deined on a sample space must follow. See Probability

• Bayesâ€™ theorem

An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Cumulative normal distribution function

The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

• Defect

Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

• Deining relation

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

• Density function

Another name for a probability density function

• Dispersion

The amount of variability exhibited by data

• Error mean square

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

• 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.

• 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.

• False alarm

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

• Fisherâ€™s least signiicant difference (LSD) method

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

• Forward selection

A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

• 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

• Generator

Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

• Geometric random variable

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

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