Solutions for Chapter 3: Mathematical Statistics with Applications 7th Edition

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.

A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

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 portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

The joint probability distribution of two random variables.

When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

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.

Another term for the conidence coeficient.

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

A continuous random variable with range of a inite interval and a constant probability density function.

See Control chart.

A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

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).

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

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

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

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.

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 .