- 12-1.1: Use ANOVA to test for any significant differences between the means
- 12-1.2: What is the purpose of this study?
- 12-1.3: Explain why separate t tests are not accepted in this situation.
- 12-1.1: What test is used to compare three or more means?
- 12-1.2: State three reasons why multiple t tests cannot be used to compare ...
- 12-1.3: What are the assumptions for ANOVA?
- 12-1.4: Define between-group variance and within-group variance.
- 12-1.5: What is the F test formula for comparing three or more means?
- 12-1.6: State the hypotheses used in the ANOVA test.
- 12-1.7: When there is no significant difference among three or more means, ...
- 12-1.8: For Exercises 8 through 19, assume that all variables are normally ...
- 12-1.9: For Exercises 8 through 19, assume that all variables are normally ...
- 12-1.10: For Exercises 8 through 19, assume that all variables are normally ...
- 12-1.11: For Exercises 8 through 19, assume that all variables are normally ...
- 12-1.12: For Exercises 8 through 19, assume that all variables are normally ...
- 12-1.13: For Exercises 8 through 19, assume that all variables are normally ...
- 12-1.14: For Exercises 8 through 19, assume that all variables are normally ...
- 12-1.15: For Exercises 8 through 19, assume that all variables are normally ...
- 12-1.16: For Exercises 8 through 19, assume that all variables are normally ...
- 12-1.17: For Exercises 8 through 19, assume that all variables are normally ...
- 12-1.18: For Exercises 8 through 19, assume that all variables are normally ...
- 12-1.19: For Exercises 8 through 19, assume that all variables are normally ...
Solutions for Chapter 12-1: Analysis of Variance
Full solutions for Elementary Statistics: A Step by Step Approach | 7th Edition
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
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
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
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
The joint probability distribution of two random variables.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
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.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
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.
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.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Discrete random variable
A random variable with a inite (or countably ininite) range.
The amount of variability exhibited by data
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.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
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
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 .
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