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# Solutions for Chapter 12: Hypothesis Testing

## Full solutions for Mathematical Statistics with Applications | 8th Edition

ISBN: 9780321807090

Solutions for Chapter 12: Hypothesis Testing

Solutions for Chapter 12
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##### ISBN: 9780321807090

This textbook survival guide was created for the textbook: Mathematical Statistics with Applications, edition: 8. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780321807090. Chapter 12: Hypothesis Testing includes 1 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 1 problems in chapter 12: Hypothesis Testing have been answered, more than 280 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• `-error (or `-risk)

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

• 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

• Average run length, or ARL

The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

• Bivariate normal distribution

The joint distribution of two normal random variables

• 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.

• 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 test

Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

• Conditional probability mass function

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

• Consistent estimator

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

• Continuity correction.

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

• Continuous distribution

A probability distribution for a continuous random variable.

• Discrete uniform random variable

A discrete random variable with a inite range and constant probability mass function.

• Error mean square

The error sum of squares divided by its number of degrees of freedom.

• Experiment

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

• Forward selection

A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

• Gamma random variable

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

• Gaussian distribution

Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

• Generating function

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

• Geometric mean.

The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .

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