- 12.1: Measures of Voltage The author measured voltage amounts from three ...
- 12.2: Based on the conclusion from Exercise 1, can electrical appliances ...
- 12.3: For the analysis of variance test described in Exercise 1, is that ...
- 12.4: Identify the value of the test statistic in the display included wi...
- 12.5: The displayed result from Exercise 1 are from oneway analysis of va...
- 12.6: In general, what is oneway analysis of variance used for?
- 12.7: What is the fundamental difference between oneway analysis of varia...
- 12.8: Given below is a Minitab display resulting from twoway analysis of ...
- 12.9: Using the same results given in Exercise 8, does it appear that the...
- 12.10: Using the same results given in Exercise 8, does it appear that the...
Solutions for Chapter 12: Analysis of Variance
Full solutions for Elementary Statistics | 12th Edition
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
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.
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
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.
A subset of effects in a fractional factorial design that deine the aliases in the design.
Another name for a probability density function
The amount of variability exhibited by data
Error mean square
The error sum of squares divided by its number of degrees of freedom.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
A signal from a control chart when no assignable causes are present
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
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
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.