- 11.4.38: The accompanying data resulted from an experimentto study the natur...
- 11.4.39: The accompanying data resulted from a 23 experimentwith three repli...
- 11.4.40: In a study of processes used to remove impurities fromcellulose goo...
- 11.4.41: As with many dried products, sun-dried tomatoes canexhibit an undes...
- 11.4.42: The following data on power consumption in electricfurnaceheats (kW...
- 11.4.43: The article Statistical Design and Analysis ofQualification Test Pr...
- 11.4.44: a. In a 24 experiment, suppose two blocks are to beused, and it is ...
- 11.4.45: a. An experiment was carried out to investigate theeffects on audio...
- 11.4.46: In an experiment involving four factors (A, B, C, and D)and four bl...
- 11.4.47: a. In a seven-factor experiment sA,, Gd, suppose a quarter-replicat...
- 11.4.48: The article Applying Design of Experiments toImprove a Laser Weldin...
- 11.4.49: A half-replicate of a 25 experiment to investigate theeffects of he...
Solutions for Chapter 11.4: 2p Factorial Experiments
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
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
Adjusted R 2
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.
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
See Arithmetic mean.
Bivariate normal distribution
The joint distribution of two normal random variables
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.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
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.
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
A study in which a sample from a population is used to make inference to the population. See Analytic study
The variance of an error term or component in a model.
Estimate (or point estimate)
The numerical value of a point estimator.
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
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.