- 11.2.16: In an experiment to assess the effects of curing time(factorA) and ...
- 11.2.17: The article Towards Improving the Properties ofPlaster Moulds and C...
- 11.2.18: The accompanying data resulted from an experiment toinvestigate whe...
- 11.2.19: A two-way ANOVA was carried out to assess the impactof type of farm...
- 11.2.20: The article Fatigue Limits of Enamel Bonds withMoist and Dry Techni...
- 11.2.21: In an experiment to investigate the effect of cement factor(number ...
- 11.2.22: A study was carried out to compare the writing lifetimesof four pre...
- 11.2.23: The accompanying data was obtained in an experimentto investigate w...
- 11.2.24: a. Show that E(Xi?? 2 X???) 5 ai, so that Xi?? 2 X??? is anunbiased...
- 11.2.25: Show how a 100s1 2 ad% t CI for ai 2 ai9 can beobtained. Then compu...
- 11.2.26: When both factors are random in a two-way ANOVAexperiment with K re...
Solutions for Chapter 11.2: Two-Factor ANOVA with Kij . 1
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
All possible (subsets) regressions
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
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
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
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
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.
Formulas used to determine the number of elements in sample spaces and events.
Another name for a probability density function
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
A study in which a sample from a population is used to make inference to the population. See Analytic study
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 series of tests in which changes are made to the system under study
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.
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.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on