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Solutions for Chapter 6.2: Elementary Statistics 12th Edition

Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola

Full solutions for Elementary Statistics | 12th Edition

ISBN: 9780321836960

Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola

Solutions for Chapter 6.2

Solutions for Chapter 6.2
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Textbook: Elementary Statistics
Edition: 12
Author: Mario F. Triola
ISBN: 9780321836960

Chapter 6.2 includes 50 full step-by-step solutions. Elementary Statistics was written by and is associated to the ISBN: 9780321836960. Since 50 problems in chapter 6.2 have been answered, more than 161845 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Elementary Statistics, edition: 12. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
  • 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.

  • 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

  • Arithmetic mean

    The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

  • Assignable cause

    The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

  • Bivariate normal distribution

    The joint distribution of two normal random variables

  • Categorical data

    Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

  • Central composite design (CCD)

    A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.

  • Central limit theorem

    The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

  • 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.

  • 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.

  • Conditional mean

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

  • Correction factor

    A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

  • Covariance

    A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

  • 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.

  • 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).

  • 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.

  • 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.

  • 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.

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