- 10.8.1: . Suppose that (X1, Y1), . . . , (Xn, Yn) are i.i.d. pairs of rando...
- 10.8.2: Consider again the data in Example 10.8.4. Test the hypotheses (10....
- 10.8.3: Consider again the data in Example 10.8.4. Test the hypotheses (10....
- 10.8.4: In an experiment to compare the effectiveness of two drugs A and B ...
- 10.8.5: Consider again the data in Exercise 4. Test the hypothesis that the...
- 10.8.6: Consider again the data in Exercise 4. Test the hypothesis that the...
- 10.8.7: Suppose that X1,...,Xm form a random sample of m observations from ...
- 10.8.8: Consider again the conditions of Exercise 7. Describe how to carry ...
- 10.8.9: Consider again the conditions of Exercise 7. Describe how to carry ...
- 10.8.10: Consider again the conditions of Exercise 9. Describe how to use th...
- 10.8.11: Let X1,...,Xm and Y1,...,Yn be the observations in two samples, and...
- 10.8.12: . Let X1,...,Xm be i.i.d. with c.d.f. F independently of Y1,...,Yn,...
- 10.8.13: Under the conditions of Exercise 12, prove that Eq. (10.8.6) gives ...
- 10.8.14: Under the conditions of Exercises 12 and 13, suppose further that F...
- 10.8.15: Consider again the conditions of Exercise 1. This time, let Di = Xi...
- 10.8.16: In an experiment to compare two different materials A and B that mi...
Solutions for Chapter 10.8: Categorical Data and Nonparametric Methods
Full solutions for Probability and Statistics | 4th Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
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
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
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
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
Coeficient of determination
See R 2 .
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
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.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
A subset of effects in a fractional factorial design that deine the aliases in the design.
A matrix that provides the tests that are to be conducted in an experiment.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
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
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.
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 .