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# Solutions for Chapter Chapter 25: One-Way Analysis of Variance: Comparing Several Means

## Full solutions for The Basic Practice of Statistics | 4th Edition

ISBN: 9780716774785

Solutions for Chapter Chapter 25: One-Way Analysis of Variance: Comparing Several Means

Solutions for Chapter Chapter 25
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##### ISBN: 9780716774785

The Basic Practice of Statistics was written by and is associated to the ISBN: 9780716774785. This textbook survival guide was created for the textbook: The Basic Practice of Statistics, edition: 4. Since 41 problems in chapter Chapter 25: One-Way Analysis of Variance: Comparing Several Means have been answered, more than 7528 students have viewed full step-by-step solutions from this chapter. Chapter Chapter 25: One-Way Analysis of Variance: Comparing Several Means includes 41 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
• 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

• 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.

• Assignable cause

The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

• 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.

• 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.

• Chi-square (or chi-squared) random variable

A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

• Combination.

A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

• Comparative experiment

An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

• Conditional probability density function

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

• Continuous random variable.

A random variable with an interval (either inite or ininite) of real numbers for its range.

• Convolution

A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

• 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.

• Correction factor

A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

• Curvilinear regression

An expression sometimes used for nonlinear regression models or polynomial regression models.

• Deming

W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

• Error variance

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

• Finite population correction factor

A term in the formula for the variance of a hypergeometric random variable.

• Fixed factor (or fixed effect).

In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

• Fraction defective

In statistical quality control, that portion of a number of units or the output of a process that is defective.

• Harmonic mean

The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .

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