Solutions for Chapter 3.4: Elementary Statistics 12th Edition

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, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

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

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

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 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 distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

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

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

An expression sometimes used for nonlinear regression models or polynomial regression models.

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

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

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

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.

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.

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

A function used in the probability density function of a gamma random variable that can be considered to extend factorials

The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .

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.