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# Solutions for Chapter 8-3: t Test for a Mean

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

ISBN: 9780073386102

Solutions for Chapter 8-3: t Test for a Mean

Solutions for Chapter 8-3
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##### ISBN: 9780073386102

Since 20 problems in chapter 8-3: t Test for a Mean have been answered, more than 24607 students have viewed full step-by-step solutions from this chapter. Elementary Statistics: A Step by Step Approach 8th ed. was written by and is associated to the ISBN: 9780073386102. Chapter 8-3: t Test for a Mean includes 20 full step-by-step solutions. This textbook survival guide was created for the textbook: Elementary Statistics: A Step by Step Approach 8th ed., edition: 8. This expansive textbook survival guide covers the following chapters and their solutions.

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

• 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.

• Center line

A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

• Continuous distribution

A probability distribution for a continuous random variable.

• 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 .

• 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 .

• Covariance

A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

• Covariance matrix

A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

• Defects-per-unit control chart

See U chart

• Dependent variable

The response variable in regression or a designed experiment.

• Discrete random variable

A random variable with a inite (or countably ininite) range.

• Dispersion

The amount of variability exhibited by data

• Enumerative study

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

• Erlang random variable

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

• Estimate (or point estimate)

The numerical value of a point estimator.

• Fixed factor (or fixed effect).

In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

• 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 function

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

• Generator

Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

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