Solutions for Chapter 14.2: Confidence and Prediction Intervals

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

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.

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

Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

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

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.

The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

The probability mass function of the conditional probability distribution of a discrete random variable.

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

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.

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

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

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

A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model

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.