- 9.5.1: Construct a sign table for the principal fraction for a 24 design. ...
- 9.5.2: Give an example of a factorial experiment in which failure to rando...
- 9.5.3: A chemical reaction was run using two levels each of temperature (A...
- 9.5.4: The article Efficient Pyruvate Production by a Multi-Vitamin Auxotr...
- 9.5.5: The article cited in Exercise 4 also investigated the effects of th...
- 9.5.6: A metal casting process for the production of turbine blades was st...
- 9.5.7: The article An Investigation into the Ball Burnishing of Aluminium ...
- 9.5.8: In a 2p design with one replicate per treatment, it sometimes happe...
- 9.5.9: Safety considerations are important in the design of automobiles. T...
- 9.5.10: In a small-disc test a small, disc-shaped portion of a component is...
- 9.5.11: The article Factorial Design for Column Flotation of Phosphate Wast...
- 9.5.12: The article An Application of Fractional Factorial Designs (M. Kilg...
- 9.5.13: In a 251 design (such as the one in Exercise 12) what does the esti...
Solutions for Chapter 9.5: 2p Factorial Experiments
Full solutions for Statistics for Engineers and Scientists | 4th Edition
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
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.
Bivariate normal distribution
The joint distribution of two normal random variables
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
Coeficient of determination
See R 2 .
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
Another term for the conidence coeficient.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A probability distribution for a continuous random variable.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
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.
Another name for factors that are arranged in a factorial experiment.
Discrete random variable
A random variable with a inite (or countably ininite) range.
A series of tests in which changes are made to the system under study
A signal from a control chart when no assignable causes are present
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.