 1.1.1: How is a sample related to a population?
 1.1.1E: How is a sample related to a population?
 1.1.2: Why is a sample used more often than a population?
 1.1.2E: Why is a sample used more often than a population?
 1.1.3: What is the difference between a parameter and a statistic?
 1.1.3E: What is the difference between a parameter and a statistic?
 1.1.4: What are the two main branches of statistics?
 1.1.4E: What are the two main branches of statistics?
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 1.1.21: Graphical Analysis In Exercises 2124, use the Venn diagram to ident...
 1.1.21E: Graphical Analysis In Exercise, use the Venn diagram to identify th...
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 1.1.23: Graphical Analysis In Exercises 2124, use the Venn diagram to ident...
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 1.1.24: Graphical Analysis In Exercises 2124, use the Venn diagram to ident...
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 1.1.25: Identifying Populations and Samples In Exercises 2534, identify the...
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 1.1.35E: Distinguishing Between a Parameter and a Statistic In Exercise, det...
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 1.1.46EC: Sleep Deprivation In a recent study, volunteers who had 8 hours of ...
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Solutions for Chapter 1.1: An Overview of Statistics
Full solutions for Elementary Statistics: Picturing the World  6th Edition
ISBN: 9780321911216
Solutions for Chapter 1.1: An Overview of Statistics
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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

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

Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

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

Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

Bayes’ estimator
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

Chisquare (or chisquared) 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.

Confounding
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.

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

Correlation coeficient
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

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 .

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff between false alarms and the detection of assignable causes.

Deming
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

Discrete distribution
A probability distribution for a discrete random variable

Expected value
The expected value of a random variable X is its longterm 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.

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.

Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .