- 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
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
A distribution with two modes
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.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
See Control chart.
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 .
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.
An expression sometimes used for nonlinear regression models or polynomial regression models.
The response variable in regression or a designed experiment.
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.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
Exponential random variable
A series of tests in which changes are made to the system under study
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.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .
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 .