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# Solutions for Chapter 23: Comparing Means

## Full solutions for Stats Modeling the World | 4th Edition

ISBN: 9780321854018

Solutions for Chapter 23: Comparing Means

Solutions for Chapter 23
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##### ISBN: 9780321854018

Chapter 23: Comparing Means includes 48 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 48 problems in chapter 23: Comparing Means have been answered, more than 21619 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Stats Modeling the World, edition: 4. Stats Modeling the World was written by and is associated to the ISBN: 9780321854018.

Key Statistics Terms and definitions covered in this textbook
• 2 k p - factorial experiment

A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

• a-error (or a-risk)

In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

• 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

• 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.

• Biased estimator

Unbiased estimator.

• Conditional probability

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

• 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

• Continuous uniform random variable

A continuous random variable with range of a inite interval and a constant probability density function.

• Control limits

See Control chart.

• 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 .

• Defect concentration diagram

A quality tool that graphically shows the location of defects on a part or in a process.

• Empirical model

A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

• Erlang random variable

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

• Experiment

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

• Extra sum of squares method

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

• 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.

• Gamma random variable

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

• Geometric random variable

A discrete random variable that is the number of Bernoulli trials until a success occurs.

• Hat matrix.

In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .

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