# Solutions for Chapter 13: The Analysis of Variance

## Full solutions for Mathematical Statistics with Applications | 7th Edition

ISBN: 9780495110811

Solutions for Chapter 13: The Analysis of Variance

Solutions for Chapter 13
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##### ISBN: 9780495110811

This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7th. Chapter 13: The Analysis of Variance includes 85 full step-by-step solutions. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. This expansive textbook survival guide covers the following chapters and their solutions. Since 85 problems in chapter 13: The Analysis of Variance have been answered, more than 80762 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• Additivity property of x 2

If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

• All possible (subsets) regressions

A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

• Average

See Arithmetic mean.

• Bayesâ€™ theorem

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

• Bivariate distribution

The joint probability distribution of two random variables.

• 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.

• Components of variance

The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

• Conditional probability distribution

The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

• Conditional probability mass function

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

• Control chart

A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

• 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.

• Counting techniques

Formulas used to determine the number of elements in sample spaces and events.

• 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.

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Defects-per-unit control chart

See U chart

• Deining relation

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

• Eficiency

A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

• Exponential random variable

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

• Fraction defective control chart

See P chart

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