Solutions for Chapter 3: Discrete Probability Distributions

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).

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.

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.

A set of rules that probabilities deined on a sample space must follow. See Probability

A distribution with two modes

When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

A probability distribution for a continuous random variable.

Formulas used to determine the number of elements in sample spaces and events.

A quality tool that graphically shows the location of defects on a part or in a process.

Another name for a probability density function

The response variable in regression or a designed experiment.

A probability distribution for a discrete random variable

A discrete random variable with a inite range and constant probability mass function.

Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

Another name for a cumulative distribution function.

A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

See P chart