Introduction to Probability 1st Edition - Solutions by Chapter

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

In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II 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

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.

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

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

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.

The probability density function of the conditional probability distribution of a continuous random variable.

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

See Control chart.

In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

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

A probability distribution for a discrete random variable

A discrete random variable with a inite range and constant probability mass function.

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

A series of tests in which changes are made to the system under study

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

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 .