Mathematical Statistics with Applications 7th Edition - Solutions by Chapter

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

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.

See Arithmetic mean.

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.

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 tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

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.

The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

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).

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.

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

A discrete random variable with a inite range and constant probability mass function.

Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

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 series of tests in which changes are made to the system under study

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

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.

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

The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .