Stats Modeling the World 4th Edition - Solutions by Chapter

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

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

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.

The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

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

Another term for the conidence coeficient.

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

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).

Formulas used to determine the number of elements in sample spaces and events.

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.

In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

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

The variance of an error term or component in a model.

The numerical value of a point estimator.

A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

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

Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

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