Solutions for Chapter 3.4: Elementary Statistics 12th Edition

A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

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

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 probability density function of the conditional probability distribution of a continuous random variable.

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

Another term for the conidence coeficient.

A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

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.

The response variable in regression or a designed experiment.

A random variable with a inite (or countably ininite) range.

The amount of variability exhibited by data

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

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

A signal from a control chart when no assignable causes are present

A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.