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# Solutions for Chapter 11: Goodness of Fit Tests and Categorical Data Analysis

## Full solutions for Introduction to Probability and Statistics for Engineers and Scientists | 5th Edition

ISBN: 9780123948113

Solutions for Chapter 11: Goodness of Fit Tests and Categorical Data Analysis

Solutions for Chapter 11
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##### ISBN: 9780123948113

This expansive textbook survival guide covers the following chapters and their solutions. Introduction to Probability and Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780123948113. This textbook survival guide was created for the textbook: Introduction to Probability and Statistics for Engineers and Scientists, edition: 5. Chapter 11: Goodness of Fit Tests and Categorical Data Analysis includes 25 full step-by-step solutions. Since 25 problems in chapter 11: Goodness of Fit Tests and Categorical Data Analysis have been answered, more than 7897 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.

• 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

• Alias

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Alternative hypothesis

In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

• Average

See Arithmetic mean.

• Bayes’ theorem

An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

• Conditional mean

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

• Conidence coeficient

The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

• 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

In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

• Covariance

A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

• 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.

• Cumulative normal distribution function

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

• Deining relation

A subset of effects in a fractional factorial design that deine the aliases in the design.

• Discrete random variable

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

• Erlang random variable

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

• 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.

• Gamma random variable

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

• 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.

• Goodness of fit

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

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