Solutions for Chapter 2: Elementary Statistics: A Step By Step Approach 9th Edition

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).

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.

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Unbiased estimator.

The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

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

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

A probability distribution for a continuous random variable.

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

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 model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

The numerical value of a point estimator.

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.

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

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

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.