Solutions for Chapter 4: Probability and Statistics for Engineers and the Scientists 9th Edition

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

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).

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.

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.

Unbiased estimator.

The joint distribution of two normal random variables

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.

Another term for the conidence coeficient.

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.

A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

Another name for a probability density function

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 continuous random variable that is the sum of a ixed number of independent, exponential random variables.

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

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 .