- 12.1E: Suppose that you wish to compare the means for two populations and ...
- 12.3E: Suppose, as in Exercise 12.1, that two populations have respective ...
- 12.2E: Refer to Exercise 12.1. Suppose that you allocate n1 = n2 observati...
- 12.4E: Refer to Exercise 12.3. How many observations are needed for a 95% ...
- 12.5E: Suppose that we wish to study the effect of the stimulant digitalis...
- 12.6E: Refer to Exercise 12.5. Consider two methods for selecting the dosa...
- 12.7E: Refer to Exercise 12.5. Why might it be advisable to assign one or ...
- 12.8E: The standard error of the estimator in a simple linear regression m...
- 12.9E: Consider the data analyzed in Examples 12.2 and 12.3.a Assuming tha...
- 12.10E: Two computers often are compared by running a collection of various...
- 12.11E: d Based on the discussion in the text and your answers to parts (a)...
- 12.12E: Refer to Exercise 12.11. Assume that ? 2 1 = ? 2 2 = ? 2. The table...
- 12.13E: Exercise 10.76 describes a dental experiment conducted to investiga...
- 12.14E: Two procedures for sintering copper are to be compared by testing e...
- 12.15E: A plant manager, in deciding whether to purchase a machine of desig...
- 12.16E: “Muck” is the rich, highly organic type of soil that serves as the ...
- 12.18E: Two drugs, A and B, are to be applied to five rats each. Suppose th...
- 12.19E: Refer to Exercise 12.18. Suppose that the experiment involved three...
- 12.20E: A chemical engineer has two catalysts and three temperature setting...
- 12.21E: Give two reasons for utilizing randomization in an experiment.
- 12.22E: What is a factor?
- 12.23E: What is a treatment?
- 12.25E: If you were to design an experiment, what part of the design proced...
- 12.26E: An experiment is to be conducted to compare the effect of digitalis...
- 12.27E: Complete the assignment of treatments for the following 3 × 3 Latin...
- 12.28SE: How can one measure the information in a sample pertinent to a spec...
- 12.29SE: What is a random sample?
- 12.30SE: What factors affect the quantity of information in an experiment? W...
- 12.31SE: Refer to the matched-pairs experiment of Section 12.3 and assume th...
- 12.33SE: Refer to Exercise 12.31. Suppose that a completely randomized desig...
- 12.34SE: Persons submitting computing jobs to a computer center usually are ...
- 12.35SE: The earth’s temperature affects seed germination, crop survival in ...
- 12.36SE: An experiment was conducted to compare mean reaction time to two ty...
- 12.37SE: Suppose that you wish to fit the model
Solutions for Chapter 12: Mathematical Statistics with Applications 7th Edition
Full solutions for Mathematical Statistics with Applications | 7th Edition
a-error (or a-risk)
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 a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
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.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
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.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
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.
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
A property of a collection of events that indicates that their union equals the sample space.
A series of tests in which changes are made to the system under study
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
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 .