- 11.3.1: Statistical Literacy Does the x distribution need to be normal in o...
- 11.3.2: Critical Thinking The x distribution must be normal in order to use...
- 11.3.3: Archaeology: Chaco Canyon The following problem is based on informa...
- 11.3.4: Sociology: Marriage The following problem is based on information f...
- 11.3.5: Mountain Climbing: Accidents The following problem is based on info...
- 11.3.6: Professors: Salaries The following problem is based on information ...
- 11.3.7: Medical: Clinical Test A new kind of typhoid shot is being develope...
- 11.3.8: Veterinary Science: Tranquilizer Jim Mead is a veterinarian who vis...
- 11.3.9: Engineering: Jet Engines The fan blades on commercial jet engines m...
- 11.3.10: Law: Bar Exam A factor in determining the usefulness of an examinat...
- 11.3.11: Engineering: Solar Batteries A set of solar batteries is used in a ...
Solutions for Chapter 11.3: CHI-SQUARE AND F DISTRIBUTIONS
Full solutions for Understandable Statistics | 9th Edition
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
Box plot (or box and whisker plot)
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).
Central limit theorem
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.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
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.
Another name for factors that are arranged in a factorial experiment.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
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.
A property of a collection of events that indicates that their union equals the sample space.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
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 .
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.
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 .
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .