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Solutions for Chapter 9.10: Applied Statistics and Probability for Engineers 6th Edition
Full solutions for Applied Statistics and Probability for Engineers | 6th Edition
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
See Arithmetic mean.
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
Chi-square (or chi-squared) random variable
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.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
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.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Another name for a cumulative distribution function.
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.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
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
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .
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 .