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# Solutions for Chapter 6-5: The Central Limit Theorem

## Full solutions for Elementary Statistics | 12th Edition

ISBN: 9780321836960

Solutions for Chapter 6-5: The Central Limit Theorem

Solutions for Chapter 6-5
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##### ISBN: 9780321836960

Chapter 6-5: The Central Limit Theorem includes 25 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Elementary Statistics was written by and is associated to the ISBN: 9780321836960. Since 25 problems in chapter 6-5: The Central Limit Theorem have been answered, more than 214645 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Elementary Statistics, edition: 12.

Key Statistics Terms and definitions covered in this textbook
• Bayes’ estimator

An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

• 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.

• Cause-and-effect diagram

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

• Coeficient of determination

See R 2 .

• 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 level

Another term for the conidence coeficient.

• Correlation matrix

A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

• 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.

• 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.

• Density function

Another name for a probability density function

• Dependent variable

The response variable in regression or a designed experiment.

• Discrete uniform random variable

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

• 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).

• Erlang random variable

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

• Error variance

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

• Estimate (or point estimate)

The numerical value of a point estimator.

• 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.

• Fisher’s least signiicant difference (LSD) method

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

• 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.

• Fraction defective

In statistical quality control, that portion of a number of units or the output of a process that is defective.

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