Solutions for Chapter 3: Mathematical Statistics with Applications 7th Edition

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

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.

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.

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

A continuous random variable with range of a inite interval and a constant probability density function.

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

See U chart

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

A matrix that provides the tests that are to be conducted in an experiment.

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

A subset of a sample space.

A term in the formula for the variance of a hypergeometric random variable.

In statistical quality control, that portion of a number of units or the output of a process that is defective.

A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

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

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.