Solutions for Chapter 6: Some Continuous Probability Distributions

A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

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

The joint probability distribution of two random variables.

In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

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).

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.

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

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.

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

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

A probability distribution for a continuous random variable.

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).

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

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

The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model

A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

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