Elementary Statistics: A Step By Step Approach 9th Edition - Solutions by Chapter

If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

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

The joint distribution of two normal random variables

Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

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 tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

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.

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.

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

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).

In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

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

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

The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

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).

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

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

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 .