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# Solutions for Chapter 10.7: Categorical Data and Nonparametric Methods

## Full solutions for Probability and Statistics | 4th Edition

ISBN: 9780321500465

Solutions for Chapter 10.7: Categorical Data and Nonparametric Methods

Solutions for Chapter 10.7
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##### ISBN: 9780321500465

This expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics was written by and is associated to the ISBN: 9780321500465. Chapter 10.7: Categorical Data and Nonparametric Methods includes 17 full step-by-step solutions. This textbook survival guide was created for the textbook: Probability and Statistics, edition: 4. Since 17 problems in chapter 10.7: Categorical Data and Nonparametric Methods have been answered, more than 15867 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• 2 k factorial experiment.

A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

• 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.

• Bivariate distribution

The joint probability distribution of two random variables.

• Bivariate normal distribution

The joint distribution of two normal random variables

• Center line

A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

• 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 mass function

The probability mass function of the conditional probability distribution of a discrete random variable.

• Continuous uniform random variable

A continuous random variable with range of a inite interval and a constant probability density function.

• 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 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.

• Discrete distribution

A probability distribution for a discrete random variable

• Discrete random variable

A random variable with a inite (or countably ininite) range.

• Event

A subset of a sample space.

• Experiment

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

• Extra sum of squares method

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

• 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.

• 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.

• Geometric random variable

A discrete random variable that is the number of Bernoulli trials until a success occurs.

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