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# Solutions for Chapter 15: Nonparametric Tests

## Full solutions for Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card | 8th Edition

ISBN: 9781464158933

Solutions for Chapter 15: Nonparametric Tests

Solutions for Chapter 15
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##### ISBN: 9781464158933

Since 52 problems in chapter 15: Nonparametric Tests have been answered, more than 31810 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card, edition: 8. Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card was written by and is associated to the ISBN: 9781464158933. Chapter 15: Nonparametric Tests includes 52 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
• Analytic study

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

• 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.

• Binomial random variable

A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

• 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 tendency

The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

• 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.

• Conditional probability

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

• Confounding

When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

• 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

• Cook’s distance

In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

• 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 .

• Cumulative normal distribution function

The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

• Cumulative sum control chart (CUSUM)

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

• Density function

Another name for a probability density function

• Designed experiment

An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

• Discrete uniform random variable

A discrete random variable with a inite range and constant probability mass function.

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• F-test

Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

• Factorial experiment

A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

• First-order model

A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model

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