Solutions for Chapter 1: Data Collection

A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

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

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

A distribution with two modes

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

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.

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

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

The amount of variability exhibited by data

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.

The variance of an error term or component in a model.

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

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