Solutions for Chapter 4.1: Sample Spaces and Probability

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

See Arithmetic mean.

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

The joint probability distribution of two random variables.

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

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 portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

The mean of the conditional probability distribution of a random variable.

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

Another term for the conidence coeficient.

Formulas used to determine the number of elements in sample spaces and events.

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

See U chart

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 signal from a control chart when no assignable causes are present

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

Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

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 .

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.