Solutions for Chapter 9.5: Statistics for Engineers and Scientists 4th Edition

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 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.

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

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

The probability of an event given that the random experiment produces an outcome in another event.

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

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.

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).

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 .

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

Another name for a probability density function

The response variable in regression or a designed experiment.

A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

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

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.