- 8-1.1: Define null and alternative hypotheses, and give an example of each.
- 8-1.2: What is meant by a type I error? A type II error? How are they rela...
- 8-1.3: What is meant by a statistical test?
- 8-1.4: Explain the difference between a one-tailed and a two-tailed test.
- 8-1.5: What is meant by the critical region? The noncritical region?
- 8-1.6: What symbols are used to represent the null hypothesis and the alte...
- 8-1.7: What symbols are used to represent the probabilities of type I and ...
- 8-1.8: Explain what is meant by a significant difference.
- 8-1.9: When should a one-tailed test be used? A two-tailed test?
- 8-1.10: List the steps in hypothesis testing.
- 8-1.11: In hypothesis testing, why cant the hypothesis be proved true?
- 8-1.12: (ans) Using the z table (Table E), find the critical value (or valu...
- 8-1.13: For each conjecture, state the null and alternative hypotheses. a. ...
Solutions for Chapter 8-1: Steps in Hypothesis TestingTraditional Method
Full solutions for Elementary Statistics: A Step by Step Approach 8th ed. | 8th Edition
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
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
Coeficient of determination
See R 2 .
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
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 .
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
The response variable in regression or a designed experiment.
A matrix that provides the tests that are to be conducted in an experiment.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
The variance of an error term or component in a model.
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
A signal from a control chart when no assignable causes are present
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
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .
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