Solutions for Chapter 3.4: Measures of Relative Standing and Boxplots

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

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

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).

The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

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

Another term for the conidence coeficient.

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

The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

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

A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

A random variable with a inite (or countably ininite) range.

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

The difference between an estimated value and the true value.

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

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

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

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