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Get Full Access to Statistics - Textbook Survival Guide
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# Solutions for Chapter 9.2: Testing Hypotheses

## Full solutions for Probability and Statistics | 4th Edition

ISBN: 9780321500465

Solutions for Chapter 9.2: Testing Hypotheses

Solutions for Chapter 9.2
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##### ISBN: 9780321500465

This textbook survival guide was created for the textbook: Probability and Statistics, edition: 4. Since 13 problems in chapter 9.2: Testing Hypotheses have been answered, more than 16565 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics was written by and is associated to the ISBN: 9780321500465. Chapter 9.2: Testing Hypotheses includes 13 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
• 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

• Analytic study

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

• 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.

• Average

See Arithmetic mean.

• Biased estimator

Unbiased estimator.

• Bivariate distribution

The joint probability distribution of two random variables.

• Chance cause

The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

• Conditional probability

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

• Conidence interval

If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

• Continuous uniform random variable

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

• 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.

• Correlation matrix

A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

• Cumulative normal distribution function

The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

• Error of estimation

The difference between an estimated value and the true value.

• Estimate (or point estimate)

The numerical value of a point estimator.

• Estimator (or point estimator)

A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

• Expected value

The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

• Exponential random variable

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

• Generating function

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

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