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

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

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

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 method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

See Arithmetic mean.

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

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

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

A probability distribution for a continuous random variable.

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 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 quality tool that graphically shows the location of defects on a part or in a process.

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.

In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.

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

The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.

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

An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

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

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 .