- 9.4.1: Recycling newsprint is important in reducing waste. The article The...
- 9.4.2: A study was done to see which of four machines is fastest in perfor...
- 9.4.3: Four lighting methods were used in each of three rooms. For each me...
- 9.4.4: Three different corrosion-resistant coatings are being considered f...
- 9.4.5: The article Genotype-Environment Interactions and Phenotypic Stabil...
- 9.4.6: The article Sprinkler Technologies, Soil Infiltration, and Runoff (...
- 9.4.7: The article Bromate Surveys in French Drinking Waterworks (B. Legub...
- 9.4.8: The article Multi-objective Scheduling Problems: Determination of P...
- 9.4.9: You have been given the task of designing a study concerning the li...
- 9.4.10: An engineering professor wants to determine which subject engineeri...
Solutions for Chapter 9.4: Randomized Complete Block Designs
Full solutions for Statistics for Engineers and Scientists | 4th 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.
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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 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.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
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 measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
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 matrix that provides the tests that are to be conducted in an experiment.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass 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).
Exponential random variable
A series of tests in which changes are made to the system under study
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.
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.