- 8.1.1: For each of the following assertions, state whether it is alegitima...
- 8.1.2: For the following pairs of assertions, indicate which donot comply ...
- 8.1.3: For which of the given P-values would the null hypothesisbe rejecte...
- 8.1.4: Pairs of P-values and significance levels, a, are given.For each pa...
- 8.1.5: To determine whether the pipe welds in a nuclear powerplant meet sp...
- 8.1.6: Let m denote the true average radioactivity level (picocuriesper li...
- 8.1.7: Before agreeing to purchase a large order of polyethylenesheaths fo...
- 8.1.8: Many older homes have electrical systems that use fusesrather than ...
- 8.1.9: Water samples are taken from water used for cooling as itis being d...
- 8.1.10: A regular type of laminate is currently being used by amanufacturer...
- 8.1.11: Two different companies have applied to provide cabletelevision ser...
- 8.1.12: A mixture of pulverized fuel ash and Portland cement tobe used for ...
- 8.1.13: The calibration of a scale is to be checked by weighing a10-kg test...
- 8.1.14: A new design for the braking system on a certain type ofcar has bee...
Solutions for Chapter 8.1: Hypotheses and Test Procedures
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
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.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
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.
An expression sometimes used for nonlinear regression models or polynomial regression models.
Discrete random variable
A random variable with a inite (or countably ininite) range.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
Another name for a cumulative distribution function.
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 study in which a sample from a population is used to make inference to the population. See Analytic study
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.
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.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
In statistical quality control, that portion of a number of units or the output of a process that is defective.