Solutions for Chapter 1: WHOLE NUMBERS

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

A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

The joint probability distribution of two random variables.

A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

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.

The probability mass function of the conditional probability distribution of a discrete random variable.

Another term for the conidence coeficient.

A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

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

A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

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).

The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

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

A subset of effects in a fractional factorial design that deine the aliases in the design.

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).

The numerical value of a point estimator.

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

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

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .