Solutions for Chapter 15: Analysis of Variance

A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

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

A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

The mean of the conditional probability distribution of a random variable.

The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

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.

A matrix that provides the tests that are to be conducted in an experiment.

The amount of variability exhibited by data

A study in which a sample from a population is used to make inference to the population. See Analytic study

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

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 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 function used in the probability density function of a gamma random variable that can be considered to extend factorials