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Solutions for Chapter 5: The Standard Deviation as a Ruler and the Normal Model

Stats Modeling the World | 4th Edition | ISBN: 9780321854018 | Authors: David E. Bock, Paul F. Velleman, Richard D. De Veaux

Full solutions for Stats Modeling the World | 4th Edition

ISBN: 9780321854018

Stats Modeling the World | 4th Edition | ISBN: 9780321854018 | Authors: David E. Bock, Paul F. Velleman, Richard D. De Veaux

Solutions for Chapter 5: The Standard Deviation as a Ruler and the Normal Model

Solutions for Chapter 5
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Textbook: Stats Modeling the World
Edition: 4
Author: David E. Bock, Paul F. Velleman, Richard D. De Veaux
ISBN: 9780321854018

Stats Modeling the World was written by and is associated to the ISBN: 9780321854018. Chapter 5: The Standard Deviation as a Ruler and the Normal Model includes 50 full step-by-step solutions. This textbook survival guide was created for the textbook: Stats Modeling the World, edition: 4. Since 50 problems in chapter 5: The Standard Deviation as a Ruler and the Normal Model have been answered, more than 59916 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
  • a-error (or a-risk)

    In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

  • Acceptance region

    In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

  • 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

  • Average

    See Arithmetic mean.

  • Average run length, or ARL

    The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

  • 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.

  • 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.

  • Comparative experiment

    An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

  • Conditional probability density function

    The probability density function of the conditional probability distribution of a continuous random variable.

  • Continuous random variable.

    A random variable with an interval (either inite or ininite) of real numbers for its range.

  • Decision interval

    A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

  • 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.

  • Dispersion

    The amount of variability exhibited by data

  • 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 of estimation

    The difference between an estimated value and the true value.

  • Exhaustive

    A property of a collection of events that indicates that their union equals the sample space.

  • Harmonic mean

    The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .

  • 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 .