Solutions for Chapter 9: Comparing Two Population Means

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).

In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

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.

An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

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.

The probability density function of the conditional probability distribution of a continuous random variable.

A random variable with an interval (either inite or ininite) of real numbers for its range.

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 .

In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

An expression sometimes used for nonlinear regression models or polynomial regression models.

The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

Another name for a probability density function

A probability distribution for a discrete random variable

A series of tests in which changes are made to the system under study

The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on