Solutions for Chapter 7.3: Confidence Intervals and Sample Size for Proportions

In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

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

Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

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

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

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

See Control chart.

In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

Another name for a cumulative distribution function.

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

The error sum of squares divided by its number of degrees of freedom.

The variance of an error term or component in a model.

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.

A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r