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# Solutions for Chapter 2.5: Elementary Statistics: Picturing the World 5th Edition

## Full solutions for Elementary Statistics: Picturing the World | 5th Edition

ISBN: 9780321693624

Solutions for Chapter 2.5

Solutions for Chapter 2.5
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##### ISBN: 9780321693624

Since 28 problems in chapter 2.5 have been answered, more than 11213 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Elementary Statistics: Picturing the World, edition: 5. Chapter 2.5 includes 28 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Elementary Statistics: Picturing the World was written by and is associated to the ISBN: 9780321693624.

Key Statistics Terms and definitions covered in this textbook
• 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

• Bimodal distribution.

A distribution with two modes

• Bivariate normal distribution

The joint distribution of two normal random variables

• Block

In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

• Components of variance

The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

• 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.

• Conidence interval

If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

• Conidence level

Another term for the conidence coeficient.

• Crossed factors

Another name for factors that are arranged in a factorial experiment.

• Cumulative distribution function

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

• Deining relation

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

• Discrete uniform random variable

A discrete random variable with a inite range and constant probability mass 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.

• Empirical model

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

• 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.

• Exponential random variable

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

• 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.

• Hat matrix.

In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .

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