# Solutions for Chapter 9-1: Testing the Difference Between Two Means, Two Proportions, and Two Variances

## Full solutions for Elementary Statistics: A Step by Step Approach | 7th Edition

ISBN: 9780073534978

Solutions for Chapter 9-1: Testing the Difference Between Two Means, Two Proportions, and Two Variances

Solutions for Chapter 9-1
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##### ISBN: 9780073534978

Chapter 9-1: Testing the Difference Between Two Means, Two Proportions, and Two Variances includes 32 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Elementary Statistics: A Step by Step Approach, edition: 7. Elementary Statistics: A Step by Step Approach was written by Patricia and is associated to the ISBN: 9780073534978. Since 32 problems in chapter 9-1: Testing the Difference Between Two Means, Two Proportions, and Two Variances have been answered, more than 7629 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

• 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

• Attribute

A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

• Axioms of probability

A set of rules that probabilities deined on a sample space must follow. See Probability

• Central composite design (CCD)

A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.

• Coeficient of determination

See R 2 .

• Consistent estimator

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

• 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 .

• Covariance matrix

A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

• Decision interval

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

• Dispersion

The amount of variability exhibited by data

• Distribution free method(s)

Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

• Error variance

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

• Estimate (or point estimate)

The numerical value of a point estimator.

• Experiment

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

• Fractional factorial experiment

A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

• Frequency distribution

An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

• 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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