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# Solutions for Chapter 8: Review Execises

## Full solutions for Elementary Statistics: A Step by Step Approach 8th ed. | 8th Edition

ISBN: 9780073386102

Solutions for Chapter 8: Review Execises

Solutions for Chapter 8
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##### ISBN: 9780073386102

Elementary Statistics: A Step by Step Approach 8th ed. was written by and is associated to the ISBN: 9780073386102. This textbook survival guide was created for the textbook: Elementary Statistics: A Step by Step Approach 8th ed., edition: 8. Chapter 8: Review Execises includes 34 full step-by-step solutions. Since 34 problems in chapter 8: Review Execises have been answered, more than 31486 students have viewed full step-by-step solutions from this chapter. 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).

• 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.

• Bias

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

• Bimodal distribution.

A distribution with two modes

• Chi-square (or chi-squared) random variable

A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

• Completely randomized design (or experiment)

A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

• Conditional mean

The mean of the conditional probability distribution of a random variable.

• 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.

• Correction factor

A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

• Critical value(s)

The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

• Defect

Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

• Deining relation

A subset of effects in a fractional factorial design that deine the aliases in the design.

• 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

• Error of estimation

The difference between an estimated value and the true value.

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• 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.

• F distribution.

The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.

• Factorial experiment

A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

• Gamma function

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

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