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# Solutions for Chapter 6.15: Statistics for Engineers and Scientists 4th Edition

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

ISBN: 9780073401331

Solutions for Chapter 6.15

Solutions for Chapter 6.15
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##### ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 6.15 includes 10 full step-by-step solutions. Since 10 problems in chapter 6.15 have been answered, more than 214249 students have viewed full step-by-step solutions from this chapter. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331.

Key Statistics Terms and definitions covered in this textbook
• `-error (or `-risk)

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Bernoulli trials

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

• Categorical data

Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

• 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 mean

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

• Conditional probability

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

• 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 .

• 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.

• Dependent variable

The response variable in regression or a designed experiment.

• Error variance

The variance of an error term or component in a model.

• Event

A subset of a sample space.

• F distribution.

The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.

• 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.

• False alarm

A signal from a control chart when no assignable causes are present

• Gamma function

A function used in the probability density function of a gamma random variable that can be considered to extend factorials

• 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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