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# Solutions for Chapter 6.5: Elementary Statistics 12th Edition

## Full solutions for Elementary Statistics | 12th Edition

ISBN: 9780321836960

Solutions for Chapter 6.5

Solutions for Chapter 6.5
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##### ISBN: 9780321836960

Chapter 6.5 includes 28 full step-by-step solutions. Elementary Statistics was written by and is associated to the ISBN: 9780321836960. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Elementary Statistics, edition: 12. Since 28 problems in chapter 6.5 have been answered, more than 201151 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• 2 k p - factorial experiment

A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

• 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

• Attribute control chart

Any control chart for a discrete random variable. See Variables control chart.

• Block

In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

• C chart

An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.

• 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.

• Coeficient of determination

See R 2 .

• 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.

• 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 .

• Cumulative distribution function

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

• Deming’s 14 points.

A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

• Design matrix

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

• Dispersion

The amount of variability exhibited by data

• 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.

• Enumerative study

A study in which a sample from a population is used to make inference to the population. See Analytic study

• Fractional factorial experiment

A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

• Gamma random variable

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

• Geometric random variable

A discrete random variable that is the number of Bernoulli trials until a success occurs.

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