- 9.2.1: Let f0(x) be the p.f. of the Bernoulli distribution with parameter ...
- 9.2.2: Consider two p.d.f.s f0(x) and f1(x) that are defined as follows:
- 9.2.3: . Consider again the conditions of Exercise 2, but suppose now that...
- 9.2.4: Consider again the conditions of Exercise 2, but suppose now that i...
- 9.2.5: Suppose that X1,...,Xn form a random sample from the normal distrib...
- 9.2.6: Suppose that X1,...,Xn form a random sample from the Bernoulli dist...
- 9.2.7: Suppose that X1,...,Xn form a random sample from the normal distrib...
- 9.2.8: Suppose that a single observation X is taken from the uniform distr...
- 9.2.9: Suppose that a random sample X1,...,Xn is drawn from the uniform di...
- 9.2.10: . Suppose that X1,...,Xn form a random sample from the Poisson dist...
- 9.2.11: 1. Suppose that X1,...,Xn form a random sample from the normal dist...
- 9.2.12: Let X1,...,Xn be a random sample from the exponential distribution ...
- 9.2.13: Consider the series of examples in this section concerning service ...
Solutions for Chapter 9.2: Testing Hypotheses
Full solutions for Probability and Statistics | 4th Edition
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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
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
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.
See Arithmetic mean.
The joint probability distribution of two random variables.
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.
The probability of an event given that the random experiment produces an outcome in another event.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
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 correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
Error of estimation
The difference between an estimated value and the true value.
Estimate (or point estimate)
The numerical value of a point estimator.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
Exponential random variable
A series of tests in which changes are made to the system under study
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function