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# Solutions for Chapter 5.1: PROBABILITY RULES ## Full solutions for Statistics: Informed Decisions Using Data | 4th Edition

ISBN: 9780321757272 Solutions for Chapter 5.1: PROBABILITY RULES

Solutions for Chapter 5.1
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##### ISBN: 9780321757272

This textbook survival guide was created for the textbook: Statistics: Informed Decisions Using Data , edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Statistics: Informed Decisions Using Data was written by and is associated to the ISBN: 9780321757272. Since 120 problems in chapter 5.1: PROBABILITY RULES have been answered, more than 141023 students have viewed full step-by-step solutions from this chapter. Chapter 5.1: PROBABILITY RULES includes 120 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
• Acceptance region

In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

• 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.

• 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.

• 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

• Bayes’ theorem

An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

• 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.

• 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

• Conidence level

Another term for the conidence coeficient.

• Crossed factors

Another name for factors that are arranged in a factorial experiment.

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Density function

Another name for a probability density function

• Designed experiment

An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

• Discrete distribution

A probability distribution for a discrete random variable

• Distribution function

Another name for a cumulative distribution function.

• Eficiency

A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

• Estimate (or point estimate)

The numerical value of a point estimator.

• Exhaustive

A property of a collection of events that indicates that their union equals the sample space.

• False alarm

A signal from a control chart when no assignable causes are present

• Fraction defective control chart

See P chart

• Frequency distribution

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

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