- 15.1: If x0 = 5, and xn = 3 xn1 mod 5 find x1, x2, . . . , x10.
- 15.2: Another method of generating a random permutation, different from t...
- 15.3: Suppose that we are to observe the independent and identically dist...
- 15.4: Suppose that X1, . . . , Xn is a sample from a distribution whose v...
- 15.5: Let X1, . . . , X8 be independent and identically distributed rando...
- 15.6: The following are a students weekly exam scores. Do they prove that...
- 15.7: A baseball player has the reputation of starting slowly at the begi...
- 15.8: A group of 16 mice were exposed to 300 rads of radiation at the age...
- 15.9: Do in Chapter 12 by using a permutation test.Use the normal approxi...
- 15.10: Do in Chapter 12 by using a permutation test.Use the normal approxi...
- 15.11: Write an algorithm, similar to what was done in the text to generat...
- 15.12: Show that the discrete inverse transform algorithm for generating a...
- 15.13: Give a method for generating a random variable having density funct...
- 15.14: Give a method for generating a random variable having distribution ...
- 15.15: Give a method for generating a random variable having distribution ...
- 15.16: Suppose that the following are the generated values of 20 random va...
Solutions for Chapter 15: Simulation, Bootstrap Statistical Methods, and Permutation Tests
Full solutions for Introduction to Probability and Statistics for Engineers and Scientists | 5th Edition
Solutions for Chapter 15: Simulation, Bootstrap Statistical Methods, and Permutation TestsGet Full Solutions
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 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
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
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
Coeficient of determination
See R 2 .
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
A probability distribution for 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.
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
An expression sometimes used for nonlinear regression models or polynomial regression models.
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
Defects-per-unit control chart
See U chart
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
Distribution free method(s)
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).
Another name for a cumulative distribution function.
Estimate (or point estimate)
The numerical value of a point estimator.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
In statistical quality control, that portion of a number of units or the output of a process that is defective.