Applied Statistics and Probability for Engineers 5th Edition - Solutions by Chapter

A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

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.

See Arithmetic mean.

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

Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

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

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

A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

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 .

The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

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

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

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 term in the formula for the variance of a hypergeometric random variable.

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

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.

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .