×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide

Solutions for Chapter 11: The Analysis of Variance

Probability and Statistics for Engineers and Scientists | 4th Edition | ISBN: 9781111827045 | Authors: Anthony J. Hayter

Full solutions for Probability and Statistics for Engineers and Scientists | 4th Edition

ISBN: 9781111827045

Probability and Statistics for Engineers and Scientists | 4th Edition | ISBN: 9781111827045 | Authors: Anthony J. Hayter

Solutions for Chapter 11: The Analysis of Variance

Solutions for Chapter 11
4 5 0 265 Reviews
14
4
Textbook: Probability and Statistics for Engineers and Scientists
Edition: 4
Author: Anthony J. Hayter
ISBN: 9781111827045

This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and Scientists, edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9781111827045. Since 63 problems in chapter 11: The Analysis of Variance have been answered, more than 11778 students have viewed full step-by-step solutions from this chapter. Chapter 11: The Analysis of Variance includes 63 full step-by-step 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.

  • Biased estimator

    Unbiased estimator.

  • 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.

  • Chi-square test

    Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

  • Combination.

    A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

  • Completely randomized design (or experiment)

    A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

  • 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

  • Control chart

    A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

  • Counting techniques

    Formulas used to determine the number of elements in sample spaces and events.

  • Covariance matrix

    A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

  • 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.

  • Critical value(s)

    The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

  • 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.

  • Deming’s 14 points.

    A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

  • Estimate (or point estimate)

    The numerical value of a point estimator.

  • 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.

  • Fractional factorial experiment

    A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

  • Generating function

    A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

  • Geometric mean.

    The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .

×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide
×
Reset your password