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# Solutions for Chapter 15.6: The KruskalWallis H-Test for Completely Randomized Designs

## Full solutions for Introduction to Probability and Statistics 1 | 14th Edition

ISBN: 9781133103752

Solutions for Chapter 15.6: The KruskalWallis H-Test for Completely Randomized Designs

Solutions for Chapter 15.6
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##### ISBN: 9781133103752

Chapter 15.6: The KruskalWallis H-Test for Completely Randomized Designs includes 6 full step-by-step solutions. This textbook survival guide was created for the textbook: Introduction to Probability and Statistics 1, edition: 14. Since 6 problems in chapter 15.6: The KruskalWallis H-Test for Completely Randomized Designs have been answered, more than 9324 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Introduction to Probability and Statistics 1 was written by and is associated to the ISBN: 9781133103752.

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.

• 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).

• Cause-and-effect diagram

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

• 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.

• 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

• 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.

• Conditional probability

The probability of an event given that the random experiment produces an outcome in another event.

• Conditional probability density function

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

• Conditional variance.

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

• Consistent estimator

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

• Contingency table.

A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

• Continuous distribution

A probability distribution for a continuous random variable.

• 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 .

• Dispersion

The amount of variability exhibited by data

• Estimator (or point estimator)

A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

• 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.

• Frequency distribution

An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

• 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 .

• Geometric random variable

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

• 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 .

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