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# Solutions for Chapter 3: Propagation of Error

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

ISBN: 9780073401331

Solutions for Chapter 3: Propagation of Error

Solutions for Chapter 3
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##### ISBN: 9780073401331

Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since 23 problems in chapter 3: Propagation of Error have been answered, more than 245536 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Chapter 3: Propagation of Error includes 23 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
• 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).

• 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.

• Arithmetic mean

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

• 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.

• Backward elimination

A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

• Bias

An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

• Categorical data

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

• 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.

• Conditional probability mass function

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

• Continuous distribution

A probability distribution for a continuous random variable.

• Contour plot

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• Cumulative sum control chart (CUSUM)

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

• 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.

• Dependent variable

The response variable in regression or a designed experiment.

• Design matrix

A matrix that provides the tests that are to be conducted in an experiment.

• Discrete distribution

A probability distribution for a discrete random variable

• Experiment

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

• Fisher’s least signiicant difference (LSD) method

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

• Gamma function

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

• 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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